Question

You have a pool of 10 men and 16 women, and you need to form a 9-member coed softball team made up of four men and five women. In how many ways can you do this?

Answer 1

To form a 9-member coed softball team with four men and five women from 10 men and 16 women, calculate separate combinations for selecting men (210 ways) and women (4,368 ways) and multiply them to get the total number of possible teams, which is 917,280.

Step-by-step explanation:

To find the number of ways you can form a 9-member coed softball team with four men and five women from a pool of 10 men and 16 women, we use combinations. The key is to recognize that the selection of men and the selection of women are independent events and can be calculated separately:

• First, calculate the number of ways to choose four men out of 10, which is expressed as 10 choose 4. This can be calculated using the combination formula, C(n, k) = n! / (k!*(n-k)!).
• Second, calculate the number of ways to choose five women out of 16, which is 16 choose 5.

Once you have both numbers, multiply them together to find the total number of ways to form the team:

• 10 choose 4 = 10! / (4!*(10-4)!) = 210 ways to choose the men
• 16 choose 5 = 16! / (5!*(16-5)!) = 4,368 ways to choose the women

Therefore, the total number of ways to form the team is 210 (ways to choose men) * 4,368 (ways to choose women) = 917,280 possible teams.