The players for a Tennis Mixed Doubles match are to be chosen from

Question

The players for a Tennis Mixed Doubles match are to be chosen from among 5 men and 4 women. In how many ways can the teams for the match be formed?

(A) 40
(B) 60
(C) 80
(D) 120
(E) 160

gmatophobia · Answer

For a mixed doubles match, we need 2 men and 2 women.

2 men can be selected among 5 men in 5C2 ways = 10

2 women can be selected among 4 men in 4C2 ways = 6

Among the selected players (two men and two women) we can form 2 teams.

M_1W_1  or  M_1W_2

Total number of ways = 10 * 6 * 2 = 120

Option D

thr3at · Answer

Hello,

My answer was 240, means I am over estimating somthing but cant find out.

Can you please tell what is the issue with my approach

Approach:

Team 1: Men 5C1 and Women 4C1 = 20
 Team 2: Men 4C1 and Women 3C1 = 12

12*20= 240.

What is the issue.

gmatophobia · Answer

thr3at

You're double counting.

Let's assume

5 men are  M_1, M_2, M_3, M_4 , and  M_5 
4 women are  W_1, W_2, W_3 , and  W_4

Team 1: Men 5C1 and Women 4C1 ⇒ Let's assume you select  M_1 W_1 
Team 2: Men 4C1 and Women 3C1 ⇒ Let's assume you select  M_2 W_2

Now let's take another situation

Team 1: Men 5C1 and Women 4C1 ⇒ Let's assume you select  M_2 W_2 
Team 2: Men 4C1 and Women 3C1 ⇒ Let's assume you select  M_1 W_1

Both the teams are same.

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