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?

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

C(10,3)·C(7.7) = 120·1 = 120

--------------------------------------------

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

--------------------------------------------

(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

---------------------------------------------------

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