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  • A panel of judges consists of 6 members, including 3 men and 3 women. If the panel must be split into 2 groups with an equal number of men and women, in how many differen

A panel of judges consists of 6 members, including 3 men and 3 women. If the panel must be split into 2 groups with an equal number of men and women, in how many different ways can the groups be formed?

 

Option: 1

1


Option: 2

2


Option: 3

0


Option: 4

3


Answers (1)

best_answer

To calculate the number of different ways the panel of 6 judges can be split into 2 groups, with an equal number of men and women in each group, we can consider the following:

First, we need to select 3 men out of the 3 available men. The number of ways to select 3 men from 3 is 3 ! /(3 ! \times 0 !)=1.

Next, we need to select 3 women out of the 3 available women. The number of ways to select 3 women from 3 is 3 ! /(3 ! \times 0 !)=1.

Therefore, the number of different ways the groups can be formed is the product of the number of ways to select the men and women:

1 \times 1=1 .

Therefore, there is only 1 different way to form the groups, ensuring an equal number of men and women in each group.

Posted by

HARSH KANKARIA

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