Question

COMBINATIONS QUESTION:
In how many ways can a committee of 6 boys & 6 girls be formed from a group of 10 boys & 15 girls?

Answer 1

Probability = number of favorable ways / total number of ways

We use the formula for combination in solving for the numerator and denominator. The combination of n things taken r at a time is C = n! / (n-r)!r!
To solve for the total number of ways, we have
C = 25! / (25-12)! 12!
= 25! / 13! 12!
= 5200300 This is the denominator.

T solve for the numerator,
boys x girls
10! / (10-6)! 6! x 15! / (15-6)! 6!
210 x 5005
= 1051050 This is the numerator.

So we have 1051050 / 5200300 = 3003 / 14858 = 0.202

Answer 2

How come you multiply and not add the two cases per gender?

Answer 3

From what I understand, when the word used is 'and', you multiply it. If the word used is 'or', you add it.

Answer 4

Ohhh, okay, thank you!