The number of words from the letters of the word $'RAJASTHAN' $ by taking all the letters at a time in which vowels are alternate, are

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

If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals

If $^{20}{C_{n + 2}}{ = ^n}{C_{16}}$, then the value of $n$ is

Statement$-1:$ The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3 .$

Statement$-2:$ The number of ways of choosing any $3$ places from $9$ different  places is $^9C_3 $.

The number of ways, $16$ identical cubes, of which $11$ are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes, is