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Question
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
Solution
There are 9 men and 6 women.
A team of 6 persons is to be formed such that it consists of at least 3 women.
Consider the following table:
| Case I |
Case II |
Case III |
Case IV |
|
| 3W 3M |
4W 2M |
5W 1M |
6W – |
|
| Number of ways | 6C3 × 9C3 = 20 × 84 = 1680 |
6C4 × 9C2 = 15 × 36 = 540 |
6C5 × 9C1 = 6 × 9 = 54 |
1 |
∴ No. of ways this can be done
= 1680 + 540 + 54 + 1
= 2275
∴ 2275 teams can be formed if the team consists of at least 3 women.
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