On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
$^{20}{C_2}$
$2\;.{\;^{20}}{C_2}$
$2\;.{\;^{20}}{P_2}$
None of these
The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals
If $^{n}{P_4} = 24.{\,^n}{C_5},$ then the value of $n$ is
A committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-