Question

A soccer club has 8 female and 7 male members. For today's match, the coach wants to have 6 female and 5 male players on the grass. How many possible configurations are there? Option 1: 588 Option 2: 840 Option 3: 1176 Option 4: 1680

Answer 1

The total number of possible configurations for 6 female and 5 male soccer players selected from 8 females and 7 males is calculated by finding the combinations for each and multiplying them together, giving us 588 as the answer.

Step-by-step explanation:

The question at hand is a combinatorics problem, involving the selection of soccer players from a group for a particular formation in a match. To determine the number of possible configurations for the team, we will calculate the combinations of choosing 6 females out of 8 and 5 males out of 7, and then multiply these two numbers since the choices are independent of each other.

Female Players: The number of ways to choose 6 female players out of 8 is calculated using the combination formula which is:

aC(n, k) = n! / (k!(n-k)!)

So, for female players C(8, 6) = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = 28

Male Players: Similarly, for male players: C(7, 5) = 7! / (5! * (7-5)!) = 7! / (5! * 2!) = 21

To find the total number of configurations, we multiply the combinations of females and males together: 28 * 21 = 588.

Therefore, the total number of possible configurations is 588, making Option 1 the correct answer.

Answer 2

There are 1. 588 possible configurations.

Step-by-step explanation:

To find the number of possible configurations, we need to apply the concept of combinations. We have 8 female members and we need to choose 6, which can be done in C(8, 6) ways.

Similarly, we have 7 male members and we need to choose 5, which can be done in C(7, 5) ways. To find the total number of possible configurations, we multiply these two values together:

C(8, 6) * C(7, 5)

= 28 * 21

= 588

Therefore, there are 588 possible configurations.