Question

A blood bank needs 12 people to help with a blood drive. 17 people have volunteered. Find

how many different groups of 12 can be formed from the 17 volunteers.

Please help I don't understand!

Answer 1

6,188 different groups of 12 that can be formed from 17 volunteers.

Explanation:

To find the number of different groups of 12 that can be formed from 17 volunteers, we can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of volunteers, and r is the number of volunteers needed for each group.

In this case, n = 17 and r = 12. Substituting these values into the formula, we get:

C(17, 12) = 17! / (12! * (17 - 12)!) = (17 * 16 * 15 * 14 * 13 * 12!) / (12! * 5 * 4 * 3 * 2 * 1) = (17 * 16 * 15 * 14 * 13) / (5 * 4 * 3 * 2 * 1) = 6188

Therefore, there are to find the number of different groups of 12 that can be formed from 17 volunteers, we can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of volunteers, and r is the number of volunteers needed for each group.

In this case, n = 17 and r = 12. Substituting these values into the formula, we get:

C(17, 12) = 17! / (12! * (17 - 12)!) = (17 * 16 * 15 * 14 * 13 * 12!) / (12! * 5 * 4 * 3 * 2 * 1) = (17 * 16 * 15 * 14 * 13) / (5 * 4 * 3 * 2 * 1) = 6188

Therefore, there are 6,188 different groups of 12 that can be formed from 17 volunteers.