Question

You have 12 men and 8 women on a roster for your co-ed slo-pitch team. How many ways can you start 10 people if half have to be men and half have to be women?

A) 96
B) 120
C) 240
D) 360

Answer 1

To start 10 players with an equal number of men and women, calculate the combinations of 5 men from 12 and 5 women from 8, then multiply. However, the total obtained does not match any of the provided answer choices, indicating a possible error in the question or choices.

Step-by-step explanation:

To determine how many ways you can start 10 people on a co-ed slo-pitch team with the requirement that half must be men and half must be women, you would calculate the number of ways to choose 5 men from the 12 men available, and the number of ways to choose 5 women from the 8 women available. The number of combinations for each gender is found using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of people available, and k is the number of people to choose.

• The number of ways to choose 5 men from 12 men is C(12, 5).
• The number of ways to choose 5 women from 8 women is C(8, 5).

Now calculate these separately:

1. C(12, 5) = 12! / (5!(12 - 5)!) = 792
2. C(8, 5) = 8! / (5!(8 - 5)!) = 56

The total number of ways to choose the team is the product of the two:

792 × 56 = 44,352 ways.

However, since we only need half men and half women among the starting 10, we need to adjust the total number:

(792 × 56) / 2 = 22,176 ways.

Therefore, the correct answer is not listed in the provided options (A) 96, (B) 120, (C) 240, (D) 360. It seems there is an error in the question or answer choices.