Basic Counting Principles 1 One male and one female can be s

Basic Counting Principles

1) One male and one female can be seleced from 12 males and 8 females in ______ ways.

2) A man, a woman, and a child can be selected from 5 men and 7 women, and 10 children in ______ ways.

3) In how many different ways can 3 history and 4 sociology books be arranged on a shelf if all boooks on the same subject are kept together?

Solution

1) 12C_1* 8C1

2)5C1 * 7C1 *10C1

3)

now, assume books of each subject as a single book.
total no. of books = 2
no. of ways to arrange 2 books = 2!
similarly as previous part,3 history and 4 sociology books can be arranged in their group in 3! and 4! ways.

total no. of ways = 2! * 3! * 4!