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# Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-president if they must be of the same g

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Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-president if they must be of the same gender? Assume no one can hold both offices.

Guest Mar 18, 2015

#2
+91465
+5

I think it is 2 of the 10 boys OR 2 of the ten girls, and order counts so that is

10*9 + 10*9 = 180

or

10P2 + 10P2 = 180

Melody  Mar 19, 2015
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#1
+81027
+5

We could choose 2 of 10 boys and the same wth the girls....so we have

[C(10,2)]^2 = 2025 ways

CPhill  Mar 18, 2015
#2
+91465
+5

I think it is 2 of the 10 boys OR 2 of the ten girls, and order counts so that is

10*9 + 10*9 = 180

or

10P2 + 10P2 = 180

Melody  Mar 19, 2015

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