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Question
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
Options
94
126
128
None
Solution
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is 94.
Explanation:
Number of men = 4
Number of women = 6
We are given that the committee includes 2 men and exactly twice as many women as men.
Thus, the possible selection can be
2 men and 4 women and 3 men and 6 women.
So, the number of committee = 4C2 × 6C4 + 4C3 × 6C6
= 6 × 5 + 4 × 1
= 90 + 4
= 94
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