SOLUTION: A group of 7 memebers having a majority of boys to be formed out of 6 boys and 4 girls . The number of ways the group can be formed is a) 80 b) 100 c) 90 d) 110

Question 758434: A group of 7 memebers having a majority of boys to be formed out of 6 boys and 4 girls . The number of ways the group can be formed is
a) 80
b) 100
c) 90
d) 110
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe your answer will be 100.
the number of boys and girls in the 7 member group can be:
4 boys 3 girls
5 boys 2 girls
6 boys 1 girl

you can't have more than 6 boys since that's all that is available.
3 boys in the 7 member group would not be a majority because you would then have 4 girls.

4 boys 3 girls is calculated as 6C4 * 4C3 = 15 * 4 = 60
5 boys 2 girls is calculated as 6C5 * 4C2 = 6 * 6 = 36
6 boys 1 girl is calculated as 6C6 * 4C1 = 1 * 4 = 4

add them up together and you get 100 possible ways that the group can be formed where the boys are in the majority.

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