Question
A committee of 4 people is to be chosen from 5 married coiples.find in how many ways the committee can be chosen if:
i) everyone is equallt eligible
ii) the committee should include at least one woman
solution so far.5 couples=10 people.
To choose 4=10C4=10!/(10-4)!4!=210 ways.pls help confirm if i am correct and also help solve (ii)
i) everyone is equallt eligible
ii) the committee should include at least one woman
solution so far.5 couples=10 people.
To choose 4=10C4=10!/(10-4)!4!=210 ways.pls help confirm if i am correct and also help solve (ii)
Answers
i) 210 is correct
ii) So what we don't want is to have all-men committees
number of all men committees = C(5,4) = 5
so the number with at least one woman
= 210 - 5 = 205
ii) So what we don't want is to have all-men committees
number of all men committees = C(5,4) = 5
so the number with at least one woman
= 210 - 5 = 205
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