5 boys and 6 girls are arranged in all possible ways. Let $X$ denote the number of linear arrangements in which no two boys sit together and $Y$ denote the number of linear arrangements in which no two girls sit together. If $Z$ denote the number of ways of arranging all of them around a circular table such that no two boys sit together, then $X: Y: Z=$

The number of ways of distributing 15 apples to three persons $A, B, C$ such that $A$ and $C$ each get at least 2 apples and $B$ gets at most 5 apples, is

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is

If a five-digit number divisible by 3 is to be formed using the numbers $0,1,2,3,4$ and 5 without repetition, then the total number of ways this can be done is