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

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

The total number of words that can be formed by using all the letters of the word $ALLEN$ such that all vowels occur in alphabetical order is:

There are $10$ different letters of the English alphabet. If words of $5$ letters are formed using these letters,how many words can be formed such that at least one letter is repeated?

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is