In how many different ways can the letters of the word '$PRAISE$' be arranged?

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

The number of positive integral solutions of the equation $xyz = 90$ is equal to:

Assuming the balls to be identical except for the difference in colours,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

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 $^{th}$)

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?