There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by $66$ the number of games that the men played with the women. The number of participants is

To fill $12$ vacancies there are $25$ candidates of which five are from scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all, then the number of ways in which the selection can be made

If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $

Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is

If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation

The number of words from the letters of the word $'RAJASTHAN' $ by taking all the letters at a time in which vowels are alternate, are