In how many ways can a committee of 2 women and... - JAMB Mathematics 2010 Question
In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
A
100
B
200
C
30
D
50
correct option: b
A committee of 2 women and 3 men can be chosen from 6 men and 5 women, in \(^{5}C_{2}\) x \(^{6}C_{3}\) ways
= \(\frac{5!}{(5 - 2)!2!} \times {\frac{6!}{(6 - 3)!3!}}\)
= \(\frac{5!}{3!2!} \times {\frac{6!}{3 \times 3!}}\)
= \(\frac{5 \times 4 \times 3!}{3! \times 2!} \times {\frac{6 \times 5 \times 4 \times 3!}{3! \times 3!}}\)
= \(\frac{5 \times 4}{1 \times 2} \times {\frac{6 \times 5 \times 4}{1 \times 2 \times 3}}\)
= 10 x \(\frac{6 \times 20}{6}\)
= 200
= \(\frac{5!}{(5 - 2)!2!} \times {\frac{6!}{(6 - 3)!3!}}\)
= \(\frac{5!}{3!2!} \times {\frac{6!}{3 \times 3!}}\)
= \(\frac{5 \times 4 \times 3!}{3! \times 2!} \times {\frac{6 \times 5 \times 4 \times 3!}{3! \times 3!}}\)
= \(\frac{5 \times 4}{1 \times 2} \times {\frac{6 \times 5 \times 4}{1 \times 2 \times 3}}\)
= 10 x \(\frac{6 \times 20}{6}\)
= 200
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