The value of $r$ for which $^{20}{C_r}^{20}{C_0}{ + ^{20}}{C_{r - 1}}^{20}{C_1}{ + ^{20}}{C_{r - 2}}^{20}{C_2} + ...{ + ^{20}}{C_0}^{20}{C_r}$ is maximum is
$15$
$20$
$11$
$10$
A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women. In how many ways can this be done? How many of these committees would consist of $1$ man and $2$ women?
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
If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^n{C_{r - 1}}$$ + {\,^n}{C_r} = $
A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is
Everybody in a room shakes hand with everybody else. The total number of hand shakes is $66$. The total number of persons in the room is