Question
A commite of 4 people is to be chosen from 4 women and 5 men. The commite mus contain at most 1 woman. Calculate the number of different committees that can be formed.
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Answer to a math question A commite of 4 people is to be chosen from 4 women and 5 men. The commite mus contain at most 1 woman. Calculate the number of different committees that can be formed.
Frederik
4.656 Answers
To calculate the number of different committees that can be formed, we will consider two cases:
Case 1: Committee with 0 women
Number of ways to choose 4 people with 0 women from 5 men =\binom{5}{4} = 5
Case 2: Committee with 1 woman
Number of ways to choose 3 men and 1 woman from 4 women and 5 men =\binom{4}{1} \cdot \binom{5}{3} = 4 \cdot 10 = 40
Total number of different committees that can be formed = Number of committees with 0 women + Number of committees with 1 woman =5 + 40 = 45
\boxed{45}
Case 1: Committee with 0 women
Number of ways to choose 4 people with 0 women from 5 men =
Case 2: Committee with 1 woman
Number of ways to choose 3 men and 1 woman from 4 women and 5 men =
Total number of different committees that can be formed = Number of committees with 0 women + Number of committees with 1 woman =
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