SOLUTION: A six number coed volleyball team is chosen from a group of eight men and five women. If there must be at least one member of each gender on the team, how many different ways can t

Algebra ->  Permutations -> SOLUTION: A six number coed volleyball team is chosen from a group of eight men and five women. If there must be at least one member of each gender on the team, how many different ways can t      Log On


   

Question 1145629: A six number coed volleyball team is chosen from a group of eight men and five women. If there must be at least one member of each gender on the team, how many different ways can the team members be chosen
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
These are the possible combinations as far as gender is concerned:

5 men & 1 woman
4 men & 2 women
3 men & 3 women
2 men & 4 women
1 man & 5 woman

Here are the number of ways each combination can be chosen:

5 men & 1 woman = 8C5 * 5C1 = %288%21%2F%285%21%2A3%21%29%29+%2A+%285%21%2F%281%21%2A4%21%29%29 = 280
4 men & 2 women = 8C4 * 5C2 = %288%21%2F%284%21%2A4%21%29%29+%2A+%285%21%2F%282%21%2A3%21%29%29 = 700
3 men & 3 women = 8C3 * 5C3 = %288%21%2F%283%21%2A5%21%29%29+%2A+%285%21%2F%283%21%2A2%21%29%29 = 560
2 men & 4 women = 8C2 * 5C4 = %288%21%2F%282%21%2A6%21%29%29+%2A+%285%21%2F%284%21%2A1%21%29%29 = 140
1 man & 5 women = 8C1 * 5C5 = %288%21%2F%281%21%2A7%21%29%29+%2A+%285%21%2F%285%21%2A0%21%29%29 = 8

Adding these all together...280 + 700 + 560 + 140 + 8...there are 1688 different ways the team can be chosen.