If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
$^{m + 1}{C_4}$
$^{m - 1}{C_4}$
$3\,.{\;^{m + 2}}{C_4}$
$3\;.{\;^{m + 1}}{C_4}$
$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
Value of $r$ for which $^{15}{C_{r + 3}} = {\,^{15}}{C_{2r - 6}}$ is
The number of ways of choosing $10$ objects out of $31$ objects of which $10$ are identical and the remaining $21$ are distinct, is
If $n = ^mC_2,$ then the value of $^n{C_2}$ is given by
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