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If a committee of 3 people is to be selected from among 5 [#permalink]

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01 Dec 2005, 14:33

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If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?

all arrangements:
- first person can be selected from any of 10 people
- second person can be any of remaining 9 except first's partner - 8 ways
- third person similarly can be any of the remaining 8 except 2 partners : 6

all arrangements: 10 * 8 * 6

as we don't need to keep order, selection can be done in:
10*8*6/3! = 80 _________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

all arrangements: - first person can be selected from any of 10 people - second person can be any of remaining 9 except first's partner - 8 ways - third person similarly can be any of the remaining 8 except 2 partners : 6

all arrangements: 10 * 8 * 6

as we don't need to keep order, selection can be done in: 10*8*6/3! = 80

Duttsit. can you please explain what does "keep order" mean. I cannot understand why we divide by 3!

the desired number of ways of chosing 3 people = total ways - no of ways a couple is selected in the comittee

total = 10C3 = 120
no of ways comittees with a couple is selected = no. of ways 5 couples are selected (no of ways a person is selected from the remaining people
= 5(8C1) = 40

so the desired ways of forming comittee = 120 - 40 = 80