hemanthp wrote:

Tom is arranging his marble collection in a collectors case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must have at least one of each type, how many different ways can he arrange the case?

(A) 120

(B) 150

(C) 420

(D) 1,260

(E) 1,680

I dont agree with the OA. Lets discuss.

Given the constraints, there is 2 ways to choose the stones :

1) Take 2 each of 2 types and 1 of the third type

3 ways to choose the type for which 1 stone is to be taken

Ways to arrange = 5!/(2!x2!) = 30

Total = 30 x 3 = 90

2) Take 3 of 1 type, one each of the other types

3 ways to choose the type for which 3 stones are to be taken

Ways to arrange = 5!/3! = 20

Total = 20 x 3 = 60

So net number of ways = 150

Answer is (b) _________________

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1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

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