If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio $2:1$,then $n=$

In how many ways can a committee of $5$ members be formed from $6$ men and $4$ women such that the committee contains at least one woman?

There are $5$ types of ice creams available in a shop. $A$ child buys $6$ ice creams.
Statement-$1$: The child can buy $6$ ice creams in $^{10}C_5$ ways.
Statement-$2$: The number of ways the child can buy $6$ ice creams is equal to the number of ways to arrange $6$ '$A$'s and $4$ '$B$'s in a row.

If set $A$ contains $8$ elements,then the number of subsets of $A$ which contain at least $6$ elements is

The number of ways in which a cricket team of $11$ members can be formed out of $6$ batsmen,$6$ bowlers,$4$ all-rounders and $4$ wicket keepers by selecting at least $4$ batsmen,at least $3$ bowlers,at least $2$ all-rounders and only $1$ wicket keeper is:

Find the number of ways of selecting $9$ balls from $6$ red balls,$5$ white balls,and $5$ blue balls if each selection consists of $3$ balls of each colour.