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 C of five marbles could be drawn?  Choose the correct option.
A) 41 B) 51 C) 62 D) 72 E) 82
there will be different cases, which we will take one by one..   1)case 1 when all five colours are different-7c5=21..   2)case 2 when three different colours and 2 of same type=6c3*2=30..   3)case 3 when two different colours and 3 of same type=6c2=15..   4)case 4 when one different colours and 2 of two different colors=5c1*4!/2!2!=15...   5)case 4 when 3 of one type and 2 of other colour=1...   total C-82 ans 82
<result>E</result>
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 C of five marbles could be drawn?