Maths-

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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 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.
$P presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial end fraction$
A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.
$C presuperscript n subscript r equals space fraction numerator left parenthesis n factorial right parenthesis space over denominator left parenthesis n minus r right parenthesis factorial cross times r factorial end fraction$
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:

$T h e space t o t a l space n u m b e r space o f space d i v i s i o n s space t h a t space c a n space b e space m a d e space b e t w e e n space n space i d e n t i c a l space b a l l s space a n d space r space d i f f e r e n t space b o x e s space w i t h o u t space l e a v i n g space a n y space o f space t h e space b o x e s space e m p t y colon space C presuperscript n minus 1 end presuperscript subscript r minus 1 end subscript W e space h a v e space g i v e n space t o space d i s t r i b u t e space 8 space i d e n t i c a l space b a l l s space i n space 3 space d i s t i n c t space b o x e s comma space s o space i t space w i l l space b e space a s space f o l l o w s colon C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript S i m p l i f y i n g space t h i s comma space w e space g e t colon C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals C presuperscript 7 subscript 2 C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 factorial over denominator left parenthesis 7 minus 2 right parenthesis factorial cross times 2 factorial end fraction C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 factorial over denominator left parenthesis 5 right parenthesis factorial cross times 2 factorial end fraction C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals fraction numerator 7 cross times 6 cross times 5 factorial over denominator left parenthesis 5 right parenthesis factorial cross times 2 cross times 1 end fraction C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals 7 cross times 3 C presuperscript 8 minus 1 end presuperscript subscript 3 minus 1 end subscript equals 21$
I = 4 times,
S= 4 times,
P = 2 times,
M= 1 time
So the number of words will be:
$C presuperscript 8 subscript 4 cross times space fraction numerator left parenthesis 7 factorial right parenthesis space over denominator left parenthesis 4 right parenthesis factorial cross times 2 factorial end fraction equals 7 cross times space C presuperscript 6 subscript 4 cross times C presuperscript 8 subscript 4$

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.

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

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The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

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The correct answer is: 21

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5
21
3⁸
⁸C₃

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $theta$ with the normal to the wall and returns back elastically. If the density of water is $rho$ and its velocity is $v$ ,then the force exerted in the wall will be

An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $theta$ with the normal to the wall and returns back elastically. If the density of water is $rho$ and its velocity is $v$ ,then the force exerted in the wall will be

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line $O A$ will

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line $O A$ will

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than $C H subscript 2 end subscript C O O to the power of minus end exponent$

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at $A$ is