APPLICATIONS

7 5 - 9 0 ■ Counting Principles Solve these exercises by using the appropriate counting principle(s).

Doubles Tennis From a group of ten male and ten female tennis players, two men and women are to face each other in a men-versus-women doubles match. In how many different ways can this match be arranged?

To find:

The number of different ways the match of men-versus-women can be arranged.

Given:

2 men and 2 women are to be chosen from a group of 10 men and 10 women each.

Approach:

The order for choosing men and women is not important.

Write the formula of the number of combinations.

C(n,r)=n!r!(n−r)!

Here, n is the total number of objects and r is the number of objects chosen.

Calculation:

For both men and women substitute 10 for n and 2 for r in the above expression.