Assume that there are 11 girls and 9 boys in the neighborhood club, and a team of 6 is to be selected. How many different teams can be selected if each team must contain exactly 3 girls and 3 boys?

Why would you switch names?

http://www.jiskha.com/display.cgi?id=1329176095

So you need 3 of the 11 girls and 3 of the 9 boys

number of selections = ......

tell me what you think.

i figured it out :). thanks!

To find the number of different teams that can be selected, we need to calculate the combination, also known as "n choose k," where n is the total number of objects to choose from, and k is the number of objects to be chosen.

In this case, we have 11 girls and 9 boys, and we need to select 3 girls and 3 boys for each team. So, we need to calculate the combination of choosing 3 girls out of 11 and 3 boys out of 9.

The formula to calculate the combination is:

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

where "!" denotes factorial, and it is calculated by multiplying a number with all the positive integers below it.

Now, let's calculate the combination:

C(11, 3) = 11! / (3!(11-3)!)
= 11! / (3!8!)
= (11 * 10 * 9 * 8!) / (3! * 8!)
= (11 * 10 * 9) / (3 * 2 * 1)
= 165

C(9, 3) = 9! / (3!(9-3)!)
= 9! / (3!6!)
= (9 * 8 * 7 * 6!) / (3 * 2 * 1)
= 84

Now that we have calculated C(11, 3) and C(9, 3), we need to multiply these two combinations to find the total number of different teams that can be selected:

Total number of teams = C(11, 3) * C(9, 3)
= 165 * 84
= 13,860

Therefore, there can be 13,860 different teams selected if each team must contain exactly 3 girls and 3 boys.