Mike@Magoosh wrote:A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations of five marbles could be drawn?
(A) 41
(B) 51
(C) 62
(D) 72
(E) 82

There are 6 Cases

5 out of other 5 Marbles & (0 Green and 0Red) - Total Cases = 1

4 out of other 5 Marbles & [(0G,1R)(1G, 0R)] - Total cases = 5C4 x 2 = 10

3 out of other 5 Marbles & [(0G,2R)(1G, 1R)(2G, 1R)] - Total Cases = 5C3 x 3 = 30

2 out of other 5 Marbles & [(3G,0R)(2G, 1R)(1G, 2R)] - Total Cases = 5C2 x 3 = 30

1 out of other 5 Marbles & [(3G,1R)(2G, 2R)] - Total Cases = 5C1 x 2 = 10

0 out of other 5 Marbles & [(3G,2R)] - Total Cases = 1

Grand Total of all possibilities = 1+10+30+30+10+1 = 82

Answer: Option E