The number of ways in which $5$ male and $2$ female members of a committee can be seated around a round table so that the two female are not seated together is

The number of diagonals in an octagon is:

The Chief Ministers of $11$ States of India meet to discuss the language problem. In how many ways can they seat themselves at a round table so that the Punjab and Madras Chief Ministers sit together?

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

How many three-digit numbers can be formed from the digits $2, 3, 5, 6, 7,$ and $9$ which are divisible by $5$,given that no digit is repeated?

Let $A_1, A_2, ......, A_{11}$ be players in a team with their $T$-shirts numbered $1, 2, ......, 11$. One hundred gold coins were won by the team. These coins are to be distributed among the players such that each player $A_i$ gets at least $i$ coins,plus an additional coin (i.e.,at least $i+1$ coins). Additionally,the captain (assume $A_1$) and vice-captain (assume $A_2$) must receive at least $5$ and $3$ coins more than their $T$-shirt numbers respectively. In how many different ways can these coins be distributed?