Question
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
- 5
- 21
- 38
- 8C3
Hint:
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty.
The correct answer is: 21
A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.
![P presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial end fraction](data:image/png;base64,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)
A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.
![C presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial cross times r factorial end fraction](data:image/png;base64,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)
Here we have given the word as: MISSISSIPPI.
Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty. So:
![T h e space t o t a l space n u m b e r space o f space d i v i s i o n s space t h a t space c a n space b e space m a d e space b e t w e e n space n space i d e n t i c a l space b a l l s space a n d space r space d i f f e r e n t space b o x e s space w i t h o u t space l e a v i n g space a n y space o f space t h e space b o x e s space e m p t y colon space
C presuperscript n minus 1 end presuperscript subscript r minus 1 end subscript
W e space h a v e space g i v e n space t o space d i s t r i b u t e space 8 space i d e n t i c a l space b a l l s space i n space 3 space d i s t i n c t space b o x e s comma space s o space i t space w i l l space b e space a s space f o l l o w s colon
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript
S i m p l i f y i n g space t h i s comma space w e space g e t colon
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals C presuperscript 7 subscript 2
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 factorial over denominator left parenthesis 7 minus 2 right parenthesis factorial cross times 2 factorial end fraction
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 factorial over denominator left parenthesis 5 right parenthesis factorial cross times 2 factorial end fraction
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 cross times 6 cross times 5 factorial over denominator left parenthesis 5 right parenthesis factorial cross times 2 cross times 1 end fraction
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals 7 cross times 3
C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals 21](data:image/png;base64,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)
I = 4 times,
S= 4 times,
P = 2 times,
M= 1 time
So the number of words will be:
![C presuperscript 8 subscript 4 cross times space fraction numerator left parenthesis 7 factorial right parenthesis space over denominator left parenthesis 4 right parenthesis factorial cross times 2 factorial end fraction
equals 7 cross times space C presuperscript 6 subscript 4 cross times C presuperscript 8 subscript 4](data:image/png;base64,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)
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.
Related Questions to study
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall
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Bp06ZOXZuk8foxKpUKSqUSq1evRkVFBex2O/Lz85GQkECFKVz3e5ZloVarERUVheTk5KC62tdee40+j3QPaG5uRklJCb799ls8//zzQX2lxccmljSpq21ubu70tUmC188hxsfIkSORmpoKhmHAcRzeeustzJw5E7m5uVSwbodcLqd7RbKPu13SJ+kkRYSPpE11F5JVOwAQB+0VCgWUSiUKCgrwwQcfYMeOHXC73bcVIrGx4fP5aEOe9nZZocZJaBcpqbxxiKJSqTBt2jRkZmbi4MGDKC4uxowZM9qUORLh8Xg87Wqr9upq22vl1l1tzCTjYgAj1l4KhQJ1dXW4evUqRo0ahYcffhhTp06lEQeyVyMt2ohxQbRbXV0dqqqqMG7cOKjVashkMnp8cS4fqautqqpCXl7e4DIuxKpe+l7cHpZlqQXqcrlQXFyMnTt3Qi6XIy0trU3t7aeffoqlS5ciLi4uyHgIDfgLgoDm5mbs2rULCxYsCIrVkv3hoMtOISZ7fX291L2zg5D47bx585CWloaqqipkZ2e3SRKIi4tDVlYWRo8ejYiIiCBXC4FYrzU1NYiJiUF2dnabulqZTDb4rFqZTIba2lrs2bMHVqu1r09nQECSPOvq6nDp0iXExcUFpeMTiHVLsos1Gk2Q8Inraknhj1KpDHucQVdXyzAMMjMz8corr/T1qQwYyGyLHTt2wGg04vr16x1+LUkYAEBDaD1NvxQ8iY4hHhEFANHR0Vi8eDEEQbjjOM/2LF5xb+ieRBK8AQgRGI7j8Msvv8Dv96OgoAAajQbZ2dm0ANtut7cxAEic1Ww2o6GhIahjVCAQAMuy1MnscDjg9/vhcDiCjuP1euF0OrvUdUASvAGIx+PBiRMncPbsWbjdbixdupQ+RuKvJpMJe/bsaTNSKiIiAvv37w+q8+B5HlarFWazGZmZmTT1ned56PV6fPXVV0HLr8/ng8ViwcyZMzt9DZLgDRDIEkjaoJHuBdnZ2YiNjQ3a6JOSy7Vr12LYsGFBLWXFiIftlZWV4dSpU1i1ahViY2PDTvwRF/uUlpaisbGx09cjCV4/Rlxi2NLSQtuWAcCDDz5IeyWHQuKser0eMTEx0Ov1VPjEWo5UojU3N9MiboPBgNjYWNoSV+w4Jr5Ckj8ozTIbpPh8PjgcDnz//fc4evQopkyZgkOHDmHNmjUoKCi4a3dGZ4qxe8rClQSvn0GsSZlMBo/Hg8OHD6OyshKFhYUYM2YMNBoN9u7di6ysLERHR4et9CLarKWlBXa7HS6Xq02Kk7gGl+M4tLS0wO12o6WlBVarlWZBh3aRIsYJx3FdilxIsdp+AvlgybAVo9EIjuNQUVGBlJQUaiTU19dj27ZtGDlyJBYvXgyDwdBGKzU2NmL69OnIy8trY1yIBVv8t/r6etTU1CA3N5caF+GeC9zSxLW1tZg6dSq2bNnSqeuVNF4/gEzLsdlsOHr0KM6dO4ctW7ZApVIhMzMzyAKNiorCqlWrsH37dnz//feYMWMGHQ9FYFkWw4YNw/33398mZLZz504sW7aMtr8lhKurbWpqwocffoglS5YEpdB7vV5cu3ZN2uMNdAKBAH766Sfs2rULOTk5WL9+fbuWqFKpRHx8PB5++GHs378fKpUKY8eOpcYAWR7J6NTQulqVSoX4+HiMGjUKRqOxTaxWPDaquroaSqUSw4YNa1NX63A4pLragQxxUfh8PixbtgwTJkwIapoYDqVSiUmTJoFlWXz++ecoKSnBtGnTkJeX1+GWFSSzmXSBEmcmk4aMPYkkeL0MqXO4ceMGampqMG3aNOj1ekydOhWBQKBDTa2JVsvNzYXRaMTly5dx5swZHD16FJGRkdBoNHe18SdaTvzT00iC14uQHLeDBw/SXsnigc5324tErVYjPT0dqampyM/Ph9lsRlVVFcxmM01zD808JjWyXq8XHMfB7/eHtXY9Hg9NeQ89DkkQlepqBxDfffcdKisr8eqrr9INfld8ZaT1f0JCAuLi4pCXlwe73Y5du3ahsrKyTSKozWZDZWUlOI4LMg7CdS5wOp2w2+2oqKgIWsJJJkxoqv1dnbfkTukZSIo4x3G4efMmUlJSEB0dDY7j6FCW7uqLF4rNZsOsWbMwbty4NiOlwqW+8zyPhoYG1NbWIicnp0Op79XV1Zg8efLgSn0fqIirsPx+P65du4b//ve/aG5uRmFhIWJiYoJSyENfG6oDQh244lZmof2MyQ9pdTFixAisWbMGycnJQdO4xRAHssvlQmlpKb799lv88Y9/xLBhw4LCZeL38fl8aGpqwunTp2E2mzt9ryTB6waIUJBaBK/Xi+LiYhw8eBAPPPAAJk2ahMjIyNsew+Px0NkRRCORWWnEqUz66anVakRGRkIul4PnebS0tNA9GYnlEkjcVtzzGACtkw1XEC6Xy6FWq2ldLbnG7qyrlQSvkwQCARqSamxshNPphM1mg9VqRSAQAMMweP7555GamtpuMB/4tb7k4sWL+Pjjj1FTUwOFQoExY8Zg7dq1UCgUaGxsxP79+7Fv3z6wLAuO4/Dmm28iNzcXSqUS//73v7F3714wDIM//elPyMnJ6eW7cfdIgtcJiIP14sWLOHHiBIqLi3H+/HlUVlYCABISEvB///d/dMr37fZxfr8fFy9exN///nfMmjULmzdvpiNBgVua8OOPP8bVq1exbds2REVF4YMPPsArr7yCrVu3YuzYsXj//fexefNmXL16FadOnUJaWhpdlolfLtykRbIlCF3iicsnnC+vK9N8xEiC10k0Gg3GjRuHqKgo/PTTT9BoNIiOjobP58PcuXMxf/58Ovf1dgQCARw8eBAsy2LhwoXQ6/VB9Q92ux1FRUV46qmnkJKSAp7n8fDDD+Ozzz5DeXk5xo0bh4ULF+Lzzz+HTCbDsmXLoFAoUFlZib/97W9BQgy0NS7I+zQ2NsJsNuPdd98N6lAfalwAt74MNTU1KCgo6PT9kwTvLiG94QKBADiOw/nz52EymTBnzhxUVlbCbDZj3bp1tG71TvA8j+PHj2POnDmIiIigUQxiWNTX18PhcATFVg0GA+RyOWpra8EwDNasWQObzQZBEJCSkgKv1wuj0Yhp06a1MWY++ugjrFixok0P5FBID+T3338fjzzySFCygd/vR0VFhZT63lsQDXTp0iVcu3YNFy5cAABs374dLS0teOutt7B+/XqMHj26w7lygiCguroa58+fxxNPPEHb/s+fPx+FhYW06kt8PIZhEB0dTa3YmJgY+n+5XA6/3w+9Xo/k5OQ2I0yjoqKQlJSE0aNHw2g0Uqd1qPVM6mojIyORkpISFKslKVfSvNpeoLm5GVeuXEFZWRl++OEH6PV6TJ48Gffddx+ioqJw9uxZTJ8+HbNnz6Z+sI4iCAISEhLw6quvgmVZlJaWYuvWrcjKykJycjJ9jhhSH0sa+oghgkqeE/o6UitLpnyLeyCTMVM8z0Mul4NlWdrmlkAe64oPUhK820CWEoZh0NjYiNLSUsTExOCZZ55BSkoK4uPjoVAowPM8DAYDpk+fDqPReFeZwTKZDHFxcRg1ahSSkpIAAPn5+bQ4OysrCzzPw+VyBfkJSc5ed9NbfZElwQsDydJwOBx0UF5SUhKeeOIJqjHElfQMwyA7O5sG+e8GmUyGe+65B+Xl5dSv5vV64fP5kJiYiMTERERHR+P69et0/1dTUwOPx0MFtSvX6Ha74Xa722QaS3W1vQj5MJxOJ27cuIGvv/4aaWlpKCwspPMp2iN0OeooLMti6dKl2L17N44cOYKkpCR88sknmD17Nh2WvHbtWhw8eBDHjx9HTEwMtm/fjhkzZiA/P7/d63C5XKiqqmqzx3O73aitraXLJaG9RFCPxwOTyUSd18CtPZ7FYrmrSeShSLFaEWRJ+89//oOqqipMmTIFs2fP7pBbpLMQDXfixAl88803AG51BFi/fj0VZLfbjePHj+N///sfGIZBUlISnn/++XaHsDQ2NmLGjBkYP358m9R3MWJ3Sl1dHaqrq5GXlxc0ey1cZIOMlJo0aVKnU9+HvOCR5YZlWSiVSvj9fly5cgURERGIj49vN87ZnZAwG8dxAEDnzIr9eR6Phy6JZPJ2e3tJu92OZcuWYcOGDUhISKCRk9BrIClPLpcLZWVlOHnyJFatWoW4uDjq5wtNmSJdBEpKStDY2IjXX3+9U9c8pJdaMuvh2LFjsNvtWL58OVQqFcaNG9er58EwDNRqdbvD60gda2iK0+2Op1QqodPpEBUVRetqw8VqXS4XFAoFdDodVCoV9Ho9oqOjaSp9aKyWtI27XRiwIwxZweN5HpcuXcKhQ4dgMpmwatWqXpug3Vd0ZnHrzr7HYoaM4BHHqLgNV1VVFQoKCpCbm9tmEz6QIUt3c3MzrFYrmpub221h4ff7wXEcmpub6eiBhoYGNDU1ha2r9fv9aG5uhsvlChv/7Sh9usdrz2wnF9tdw4PJDTObzSgtLcWCBQugVqtpFklfzvTqCaxWKwoKCpCent7GuBD7JsXGhc1mQ11dHdLT04Oa9pB+LaHx3rq6Otx7770Dq65WXMUemh1Bqp9IYLorXScBUPdIcXExPvvsM8yaNQsej6fLe5T+DMMwSElJwYoVK9po8u3bt+Ppp5/G8OHD20QjQtuU2e12/OMf/8Djjz8eJMBerxdXr17tUiVarwmeuAGN0+mEw+FAeXk5zV8jzQDlcjl0Oh1SU1ORkJAAo9F41+PTxZ2VAODkyZM4d+4c1qxZg5ycnA5v0gcqpA7DYDC0ETy5XA6NRoPY2Fgaqw1X7ENGvzMMA51OF3Qcj8cDrVbbpRSpXhM8nudhsVjQ2NiIGzduBH1bQi0tp9OJmpoaaDQapKWlISsrCwkJCR120JJmN0ajEUqlEnPmzMGcOXO6ZQT7YCG0rjY0Vjvg62pJNKC8vBzXr1+Hx+Oh7gHx436/HwzD0G8ZCQ9du3YNFosFOTk5yMrKatd/RZbuhoYGHDx4EG63m7Zq0Ol0neqUNBQgGi7UiOhpelTwiFCZTCZcunQJPM9DqVTSkZUAqNCRFvbiXDRS12m321FaWgqPx4OJEye2qXoiXTB//PFHbN++HWPGjMGiRYtoEL2r+8SBBrnvXq+3jeYiExndbjdNwWpv3IDX66Wfjfg4JJbcb/PxSB/d0tJS6iQlEwmJM5PcILEgCYJAx6YTfD4fysrKoNVqkZ2dDbVaTZ2a5FiJiYnYuHEjkpKS6CZ5KEJGx1+6dKmNb7KhoQEXL15EfX39HY0r4lq5cOFCmwErVVVVbQqL7oYeEzwiFOfPn6eajuSAES86ALq0io0PYmwQq1acMVFSUgKlUomkpCRcuXIFP//8M+bNm4ekpCQkJydTbTmUl1WZTAa/3w+LxdKmrnbOnDloamoCx3FBdbVmsxmVlZXIz8+nsWm/30+9AGJDwuPxoL6+HnFxcZ0+xx7VeBUVFairqwtKJRILIABaMkfihiSmSJIZGYahexBBEMBxHEpLS3Hq1CmcPXsWs2bNoscarO6Ru4VlWZrGlZyc3K7riOyLW1tbaV1tYWEhEhISgmoyxHi9Xjgcjv5ZV0u+Rb/88kuQw5Isf0QAiTARw4L8iDWW+P9ECB0OB4YPH46NGzciOjq6TX84iV8hPVnIyNHQCT7hBqqQhAlxqzSygnXXAJYeETzSEoH4goDgBEPirCRGQXudisQXSIQUQJBvqb3KfIlfEd93cbSiI68jzxN/Nt1h9faI4AUCAdTW1lJLiAia2IIl1ihxm5C9XbiBvOEE0G63w+12D6oYa09ANBvxFoghe+pwdbUcx8Htdgf9naxO3UGPLbUkiMyyLN2/ER8eMfeBXwPa4rZYod/G0BtDqr1Cb4zELUhZ5F/+8pcOJbGS7YvVasXbb78ddsaFGL/fD5vNhhkzZnT6HHtM8MR+HiJ4ROhIirXYnUJ+iMa7XQIB2W90pev4YEapVGLv3r09fn+6str02B6PCBBZPkkFO1Hv4uxaovWIxiJfj04AAAYtSURBVCN/F/8buvxKQ5TbR6VSISEhocffp9+NDRVboMCvgkh+JxYu+b9YUMnfxPlz4QRsKDuI7wRJEujP9IjgkVgsWUrF7U6JZRWa2SAWOrHghVq85PVqtbpL7e4l+pYe+eRYlkVMTAxYlqUxWJINEeqnI4QKmjhVKpwZbzAYutQKVaJv6TGNFxMTA5VKBZfLFWS2i6udws1XCF1ixcJHfmdZFomJiZIPbwDTY4JnNBqRkJAAm80W5B4Rp1KHEzyxMSHe35HfA4EA9Ho9UlNTu1RQLNG39NjunGVZjB07FgaDgVq2YkMi3E97RoX4/wzDIC4uDsOHD5diswOYHhM8mUyG6OhoTJ06lfreiHCJhVD8EyqA4vAa+d1gMGDixInQ6XSSVTuA6dFPTqFQIDU1FdnZ2bRvW6h/L1TYgOBSRLGQarVaFBQU9IqPSqJn6VF/BHF7TJ48GQqFAleuXAnKiGjPugUQpPWAW/1EJkyYgMzMTMmNMgjotbpap9OJa9euobi4OGy6tRix8DEMg/j4eEyePBlpaWntNqqRGFj0muCRZdPtdqO0tJTWZYYmBRB3iUKhgF6vx/jx45GRkQGNRhO28YzEwKTXOwmQrFer1YqamhrYbDa4XC4aUpPL5YiMjERsbCyGDx8Og8EgablBSL9oU0aSCIBfe/RKDG76heAB4ZM+JQYv/Ua1SAI3tJA8sBJ9giR4En1Cp5Zakm1C8uzE5YXiXijiHLxwbSvEj4cbBiIxeOmU4LW0tMBiseCJJ56ATCbDgQMHEBcXR8sVq6ur8eabb+LChQsQBAHJycnYvHkzRo0aBUEQUFNTg7feegvnzp0DACQmJmLLli3IyMgY8l0Ahgp3vdT6fD6cPn0ar7/+OmQyGQ2BAb92lty5cyciIyPx0Ucf4aOPPgLDMNixYwesVitsNht27doFrVaLDz/8EDt27IBarca//vUvWK3WsBVmfr+fDgpubW2Fy+XqcitUib7lrjWez+dDREQEVq5cibKyMhQVFQX1Vrt27RquXr2K5557DiNGjIDP58ODDz6II0eOoKamBhzH4cKFC3j22WcxcuRI+P1+PPTQQzhw4ABqa2thNBqD0p0CgQDMZjOKiopQXV2NhIQEjB07FjabDfPmzeuRsUoSPc9dazy1Wo0pU6Zg+vTpbTprCoKAqqoqBAIBxMXF0XYViYmJcDgcsNlsqKiogM/nQ3x8PC36SUhIoBOuxRqPtJHduHEjnE4nCgsL0dLSgs2bN+PGjRvSkjyAuWuNJ+5vEpqISepdAdAwl0wmQ0REBFQqFS3qFj/OMAwMBgPUajUtgSS43W4UFRWhsbERGzZsQEZGBnQ6HS5duoTU1FQpH28A0+OfHBE+MqwjnJYSP04QBAGNjY3YsWMH5s2bh5SUFAC3hNFqtSIpKUkKrQ1gulXwZDIZTXUnRT6ko6dSqYRer4fRaEQgEEBraytN8HQ4HJDL5TAYDEFazGw2w2azISMjA3K5HIFAAKdPn4ZcLkdKSookeAOYuxY8YmWSNqWkBQUJ8hOXSXV1NdxuNziOw/Xr16HT6RAbG4uMjAwwDIOqqir6+I0bN6DRaBATExMkeGTZlsvldLbCO++8A5VKheTkZGmpHcB0yqptaGiA2WxGXV0dnE4nrl69Cr/fj/j4eKSkpGDy5Mn48ssvYTAYAAAHDhzAk08+ibS0NLhcLvz2t79FUVERbXe/b98+LF++HCNGjAhabnNycmAwGHDq1CnodDps27YNKpUKw4cPv2NjGYn+zV1np3Ach6NHj+LMmTNobW2FIAjQarXIysrCkiVLoNfrYbFYsGfPHpjNZjAMg5ycHCxevBgGg4G2Pd27dy9MJhNkMhmys7OxZMmSNq4Ru92OH374AV999RUEQcCCBQuwfv16rF27FqtXr+7WGyHRu/SbtKhwXLhwASdOnMCzzz4Lr9eLgwcPYvPmzdi1a1evT1iU6F769e48KSkJdXV1eOyxx2iT7t27d2PkyJF9fWoSXaRfazyfzweO49DS0kITDaKioqSeKYOAfi144mozAO2WREoMPPq14EkMXiRHmESfIAmeRJ8gCZ5EnyAJnkSfIAmeRJ8gCZ5En/D/0Hi76rqYwhsAAAAASUVORK5CYII=)
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall
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)
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then ![m subscript 1 end subscript m subscript 2 end subscript equals](data:image/png;base64,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)
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then ![m subscript 1 end subscript m subscript 2 end subscript equals](data:image/png;base64,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)
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .