The number of ways in which first,second and third prizes can be given to $5$ competitors is

In how many ways can the letters of the word $EAMCET$ be arranged such that no two vowels are together?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if there are always $4$ letters between $P$ and $S$?

Find the total number of $9$ digit numbers which have all the digits different.

The number of ways in which $n$ boys and $n$ girls can be arranged in a row such that all the boys are together and all the girls are also together is equal to