The number of ways to give away $25$ apples to $4$ boys, each boy receiving at least $4$ apples, are
$^{29}C_3$
$100$
$^{12}C_3$
$^{24}C_3$
In an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
cards are of the same colour?
In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls $?$
Let $S=\{1,2,3, \ldots ., 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_K$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_1+N_2+N_3+N_4+N_5=$