SOLUTION: Combinations 3. In how many ways can a group of 10 people be divided into (a) two groups consisting of 7 and 3 people (b) three groups consisting of 4,3 and 2 people?

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Question 841542: Combinations
3. In how many ways can a group of 10 people be divided into (a) two groups consisting of 7 and 3 people (b) three groups consisting of 4,3 and 2 people?
[ans: (a) 120 (b) 12600 ]
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
In how many ways can a group of 10 people be divided into (a) two groups consisting of 7 and 3 people 
(10 choose 3) AND THEN (7 choose 7)

C(10,3)·C(7.7) = 120·1 = 120

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Notice that it doesn't matter if you choose the 7 people first:

(10 choose 7) AND THEN (3 choose 3)

C(10,7)·C(3,3) = 120·1 = 120

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3. In how many ways can a group of 10 people be divided into (b) three groups consisting of 4,3 and 2 people?
(This means that 1 person is not chosen)

(10 choose 4) AND THEN (6 choose 3) AND THEN (3 choose 2)

C(10,4)·C(6,3)·C(3,2) = 210·20·3 = 12600

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Notice that it doesn't matter which order you choose the groups,
The numbers to multiply are different but he answer is theame
in every case

(10 choose 4) AND THEN (6 choose 2) AND THEN (4 choose 3)

C(10,4)·C(6,2)·C(4,3) = 210·15·4 = 12600

(10 choose 3) AND THEN (7 choose 2) AND THEN (3 choose 3)

C(10,3)·C(7,4)·C(3,2) = 120·35·3 = 12600

(10 choose 3) AND THEN (7 choose 2) AND THEN (3 choose 3)

C(10,3)·C(7,2)·C(5,4) = 120·21·5 = 12600

(10 choose 3) AND THEN (7 choose 2) AND THEN (3 choose 3)

C(10,2)·C(8,4)·C(4,3) = 45·70·4 = 12600

(10 choose 3) AND THEN (7 choose 2) AND THEN (3 choose 3)

C(10,2)·C(8,3)·C(5,4) = 45·56·5 = 12600

Edwin
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