How many selection of 4 books can be made from 8 different books?

How many different selections of 4 books can be made from 10 different books,if There is no restriction Tow particular books are always selected; Two particular books are never selected?

How many different selections of 6 books can be made from 11 different books, if (i) two particular books are always selected. (ii) two particular books are never selected?

How many selections and arrangementsof 4 letters can be made from the letters of the word PROPORTION?

In how many ways 7 books can be arranged from 10 books?

From 4 mangoes,5 oranges and 6 apples,how many selections can be made by taking at least one of them?