All possible two-factor products are formed from the numbers $1, 2, 3, 4, \dots, 200$. The number of products out of the total obtained which are multiples of $5$ is:

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

$A$ person wants to climb a $n$-step staircase using one step or two steps. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

How many $3$-digit numbers can be formed by using the digits $1, 3, 6,$ and $8$,when the digits may be repeated any number of times?

$A$ 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

In how many ways,a committee of $3$ members can be selected from $5$ men and $4$ women,consisting of $2$ men and $1$ woman?