A team of 4 people is going to selected from 5 couples. Find the number of ways to form the team if
a) the team consists of no couples
b) the team consists of exactly 1 couple.
Permutation and Combination Problem?
2015-12-03 5:12 pm
回答 (1)
2015-12-03 5:46 pm
a)
1. select 4 couples from 5 couples = C(5,4)
2. select 1 person from each required couple ( Total：4 couples ) = C(2,1) C(2,1) C(2,1) C(2,1)
∴ C(5,4) C(2,1) C(2,1) C(2,1) C(2,1) = 80 ways
b)
1. select 1 couples from 5 couples = C(5,1)
2. select 2 people from the required couple ( Total：1 couples ) = C(2,2)
3. select 2 couples from the remaining 4 couples = C(4,2)
4. select 1 person from each required couples ( Total：2 couples ) = C(2,1) C(2,1)
∴ C(5,1) C(2,2) C(4,2) C(2,1) C(2,1) = 120
1. select 4 couples from 5 couples = C(5,4)
2. select 1 person from each required couple ( Total：4 couples ) = C(2,1) C(2,1) C(2,1) C(2,1)
∴ C(5,4) C(2,1) C(2,1) C(2,1) C(2,1) = 80 ways
b)
1. select 1 couples from 5 couples = C(5,1)
2. select 2 people from the required couple ( Total：1 couples ) = C(2,2)
3. select 2 couples from the remaining 4 couples = C(4,2)
4. select 1 person from each required couples ( Total：2 couples ) = C(2,1) C(2,1)
∴ C(5,1) C(2,2) C(4,2) C(2,1) C(2,1) = 120
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