In how many ways can $5$ prizes be distributed among $4$ boys,if each boy can receive any number of prizes?

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

How many numbers between $999$ and $10,000$ can be formed using the digits $0, 2, 3, 6, 7, 8$ without repetition?

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

How many $6$-digit numbers can be formed using only odd digits,such that all odd digits appear at least once?

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)