In a football championship, there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is
$17$
$18$
$9$
$13$
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
In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded
The number of ways in which a committee of $6$ members can be formed from $8 $ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is
The value of ${}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}{C_3}} $ is
Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ element is :