The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
- A
$1332$
- B
$666$
- C
$333$
- D
None of these
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$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
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It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?
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The number of ways, $16$ identical cubes, of which $11$ are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes, is
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- [JEE MAIN 2022]
The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
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$\left( {\begin{array}{*{20}{c}}n\\{n - r}\end{array}} \right)\, + \,\left( {\begin{array}{*{20}{c}}n\\{r + 1}\end{array}} \right)$, whenever $0 \le r \le n - 1$is equal to
$\left( {\begin{array}{*{20}{c}}n\\{n - r}\end{array}} \right)\, + \,\left( {\begin{array}{*{20}{c}}n\\{r + 1}\end{array}} \right)$, whenever $0 \le r \le n - 1$is equal to