The number of four lettered words that can be formed from the letters of word '$MAYANK$' such that both $A$'s come but never together, is equal to

A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

The sum $\sum\limits_{i = 0}^m {\left( {\begin{array}{*{20}{c}}{10}\\i\end{array}} \right)} \,\left( {\begin{array}{*{20}{c}}{20}\\{m - i}\end{array}} \right)\,,$ $\left( {{\rm{where}}\,\left( {\begin{array}{*{20}{c}}p\\q\end{array}} \right)\, = 0\,{\rm{if}}\,p < q} \right)$, is maximum when m is

Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-