The total number of permutations of the letters of the word "$BANANA$" is

The number of groups that can be made from $5$ different green balls,$4$ different blue balls,and $3$ different red balls,if at least $1$ green and $1$ blue ball is to be included.

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that each team includes exactly $3$ bowlers and $1$ wicket-keeper?

The exponent of $3$ in $100!$ is