Answer :
The probability of all four women being on the search committee as members in it is 1/273.
We have 15 people in total out of which there are 10 men and 5 women. We need four people on the committee out of these 15.
The probability of that happening can be calculated using the formula -
= Probability of all four women getting selected/Probability of all getting selected
= (5!/4!.1!) / (15!/4!11!)
= (5!/4!1!) * (4!11!/15!)
= (5*4*3*2*1) / (15*14*13*12)
= 1/273
From this, we know that if we need to have all four women as members of the search committee, the probability of that happening is 1/273.
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