How many $3$-digit numbers can be formed by using the digits $0, 2, 3, 6, 8$ when the digits may be repeated any number of times?

Out of $13$ cricket players,$4$ are bowlers. In how many ways can a cricket team of $11$ players be formed such that at least $2$ bowlers are included?

$^nC_r \div ^nC_{r-1} = $

If ${}^n{P_5} = 20 \cdot {}^n{P_3}$,then $n = $

Three horses $H_{1}, H_{2}, H_{3}$ entered a field which has $7$ portions marked $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6}$ and $P_{7}$. If no $2$ horses are allowed to enter the same portion of the field,in how many ways can the horses graze the grass of the field?

$A$ man $X$ has $7$ friends,$4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends,$3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. The total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men,such that $3$ friends of each of $X$ and $Y$ are in this party,is: