The product of any $r$ consecutive natural numbers is always divisible by

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball is:

If ${ }^{2n}C_3 : { }^{n}C_3 = 12 : 1$,then $n =$

The total number of different combinations of one or more letters which can be made from the letters of the word $MISSISSIPPI$ is

$A$ student is allowed to select at least $(n+1)$ books but not all books from a collection of $(2n+1)$ books. If the total number of ways in which he can select these books is $255$,then the number of books in that collection is

If a person has $3$ coins of different denominations,the number of different sums that can be formed is