In how many ways can a committee of 3 women and 2 men be chosen
FURTHER MATHEMATICS
WAEC 2023
In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
- A. 500
- B. 350
- C. 720
- D. 210
Correct Answer: D. 210
Explanation
For choosing, its different 'combinations'
Options - 7 men, 5 women
To pick - 2 men, 3 women
∴ The number of ways to choose a committee of 3 women and 2 men from a group of 7 men and 5 women is:
=\(^5C_3 \times ^7C_2\)
=\(\frac{5\times4\times3}{3\times2}\times\frac{7\times6}{2\times1}\)
=\(10\times21\)
=210
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