A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to
${2^{n - 1}}$
${2^n}$
${2^{n + 1}}$
${2^{2n}}$
The number of ways in which an examiner can assign $30$ marks to $8$ questions, giving not less than $2$ marks to any question, is
In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together
A committee of $4$ persons is to be formed from $2$ ladies, $2$ old men and $4$ young men such that it includes at least $1$ lady, at least $1$ old man and at most $2$ young men. Then the total number of ways in which this committee can be formed is
If $n = ^mC_2,$ then the value of $^n{C_2}$ is given by
$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $