A committee of $11$ members is to be formed from $8$ males and $5$ females. If $m$ is the number of ways the committee is formed with at least $6$ males and $n$ is the number of ways the committee is formed with at least $3$ females, then
$n = m \,-\, 8$
$m + n = 68$
$m = n = 78$
$m = n = 68$
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
A person wants to climb a $n-$ step staircase using one step or two steps. Let $C_n$ denotes the number of ways of climbing the $n-$ step staircase. Then $C_{18} + C_{19}$ equals
The solution set of $^{10}{C_{x - 1}} > 2\;.{\;^{10}}{C_x}$ is
If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals
$^n{C_r}{ + ^n}{C_{r - 1}}$ is equal to