probability

[fossil pendant]

I am confused at how to select those woman who do not want to he in same committee. I have count the total possibility which is 8610

[solid pecan]

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[crystal jetty]

You may modify the 7C3 and 7C2 in the formula you presented, since not all those selections are feasible.

Modifying 7C2 is straightforward, since only one choice is rendered infeasible, so subtracting 1 from it suffices

For modifying 7C3, you may split the feasible selections into the following cases:

1. Choosing one of the women in refusal, and then choosing the remaining 2 committee members from the remaining 5
2. Choosing the other woman in refusal, and then choosing the remaining 2 committee members from the remaining 5
3. Choosing all 3 committee members from the other 5

Alternatively, you can subtract the infeasible cases from 7C3 as well