$^n{P_r}{ \div ^n}{C_r}$ =
$n\,!$
$(n - r)!$
$\frac{1}{{r!}}$
$r\,!$
If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$
If the different permutations of all the letter of the word $\mathrm{EXAMINATION}$ are listed as in a dictionary, how many words are there in this list before the first word starting with $\mathrm{E}$ ?
Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?
A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to
$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated is