All possible 5-digit numbers each having 5 distinct digits are formed using the digits $1,2,3,5,6,8$. Among them, the number of numbers which are divisible by 3 but not by 6 is

The total number of ways of forming a committee of 5 members out of 7 Indians, 6 Americans, 5 Russians and 4 Australians, so that every committee contains atleast one member from each country is

If $n, r$ are two positive integers such that $1 \leq r

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