Question
The value of 50C4 +
is -
- 55C4
- 55C3
- 56C3
- 56C4
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 value of 50C4 +
.
The correct answer is: 56C4
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,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAnCAYAAADjEg0YAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAAspJREFUeNrtmjFIA0EQRY9DgtiKiNiJlYUcpAgiIoKViIidtSAiYiVYWtgEsbK1EBEbC7EURFJIsElhKTYpxMJGRIIEEc5ZmIAss2aTnd3LufvgF46Xvbjjzc7MTRT5zSaozLBOGdcKMDIJumdcr4prBhg3NDH4fCr9XATdhW3lIUEHRYwOitBBxbC95hyAtgzX+CJs20xnmvdcg2YI+x5oBzQMOgF9gt5w42UahG0KdBu215wPUIGwX6AzhHNmQTFoFNQEDUjXvhOfL+DaAUO+FfYn0DphF0/RoGR77SD0BRgcFCvCVh+GOpnn4CC3Ia4EqijOFcpeDyHOHjegacm2imdPpGmPXCcJj6BFUA0f013P0uwj0BpxrcpOsYVrsxNjXD7DrCXBg9GnQvUStEBcq7I7LVRL+OS0mP7jUW3il0vxUBWp6VwOnST6cJNSptavyOD6NRxktdUj4uypRtwdBz1Ih+I8HpgTOXNQrpqlIs5uaMTdZdA5YV/DCjxviL+ZozVzoKif2JDj7JUi7u4pHFGOzHtbgT+Q46wq7orzZkmyDWEFPqh5r1RDgS4RjhiRDsZqTpOEf0crFU/xCROO2Zcc5pr0H6urVLziaFMDXabiJ2Ebepcj26lkgDcVV9Hq6VWw6zDq+HtyjVJxY300S5V6U4nEMXYd8t4d4Cbz0axSZD4tY7oBSQ87SNWvc5YYZZlIJBn/c+hCdbydOSjLRIJjlMoF1GiWs9fkuomEDThGqTgQ9xMvO0UjtoaJ0u+Xn9Rb14arTdJJJGzBMUrFgbjfC+gQNEb8nppbePehDOAYpeJA3G+lzTVySHv11UGdjlL9PrS7aUfFbdZVOejZBwdxjFJxlBnt1qVCXN0HB9kapeIuM7yd37Y1StVpmdFuXWujWb0OxyiVizIj00I1a0xHqWyXGZm3erImNEtzANcolY0zsuM22A+X3gpqcCqfvgAAAU10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW11bHRpc2NyaXB0cz48bWk+UDwvbWk+PG1pPnI8L21pPjxub25lLz48bXByZXNjcmlwdHMvPjxub25lLz48bWk+bjwvbWk+PC9tbXVsdGlzY3JpcHRzPjxtbz49PC9tbz48bW8+JiN4QTA7PC9tbz48bWZyYWM+PG1yb3c+PG1vPig8L21vPjxtaT5uPC9taT48bW8+ITwvbW8+PG1vPik8L21vPjxtbz4mI3hBMDs8L21vPjwvbXJvdz48bXJvdz48bW8+KDwvbW8+PG1pPm48L21pPjxtbz4tPC9tbz48bWk+cjwvbWk+PG1vPik8L21vPjxtbz4hPC9tbz48L21yb3c+PC9tZnJhYz48L21hdGg+nscttQAAAABJRU5ErkJggg==)
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:
![C presuperscript 50 subscript 4 plus begin inline style sum from r equals 1 to 6 of end style space C presuperscript 56 minus r end presuperscript subscript 3
S o l v i n g space t h i s comma space w e space g e t colon
C presuperscript 50 subscript 4 plus C presuperscript 50 subscript 3 plus C presuperscript 51 subscript 3 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3
N o w space u s n i n g space t h e space f o r m u l a colon
C presuperscript n subscript i plus C presuperscript n subscript i minus 1 end subscript equals C presuperscript n plus 1 end presuperscript subscript i
A p p l y i n g space t h i s comma space w e space g e t colon
C presuperscript 51 subscript 4 plus C presuperscript 51 subscript 3 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript 52 subscript 4 plus C presuperscript 52 subscript 3 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript 53 subscript 4 plus C presuperscript 53 subscript 3 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript 54 subscript 4 plus C presuperscript 54 subscript 3 plus C presuperscript 55 subscript 3
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript 55 subscript 4 plus C presuperscript 55 subscript 3
A p p l y i n g space t h e space s a m e space f o r m u l a space a g a i n comma space w e space g e t colon
C presuperscript 56 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 .
Related Questions to study
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
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.
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
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
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
![](data:image/png;base64,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)
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
![](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 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 .