5 boys and 5 girls form a line. Find the number of ways making the seating arrangement is (i) Boys and girls are alternate (ii) All the girls together

Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.

3 boys and 3 girls are to sit in a row. How many ways can this be done if (i) there are no restrictions (ii) there is a girl at each end (iii) boys and girls are at alternate palces (iv) all boys sit together

Find the number of ways of arranging letters of the word MATHEMATICAL. How many of these arrangements have all vowels together?

It is required to arrange 8 books on a shelf. Find the number of ways to do this if two specified books are (i) always together (ii) never together