Permutation and Combination - General Questions

From 7 men and 7 women, a committee of 5 is to be formed with exactly 3 men and 2 women. In how many ways can it be done?

Evaluate 6P3.

How many diagonals does a polygon with 19 sides have?

In how many ways can 6 people be seated around a circular table?

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