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
$7$
$10$
$8$
$6$
The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?
If $P(n,r) = 1680$ and $C(n,r) = 70$, then $69n + r! = $
Let $S=\{1,2,3,5,7,10,11\}$. The number of nonempty subsets of $S$ that have the sum of all elements a multiple of $3$ , is $........$
Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -