Question

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

Answer 1

total number of distinct combination is 82

Explanation:

Given data:

green marbles 3

red marbles = 2

number of distinct colors is 5

different cases of combination of 5 marbles is

case -1 when there is 5 distinct color marble -
`^7C_5 = 21`

case - 2 when there is 3 different color and two are of same color
`^6C3_ * 2 = 30`

case 3 - when 2 are of different type and 3 are of same color
`= ^6C2_ = 15`

case 4 - when 1 are of different color and 2 are of different color
`=^5C1_ * (4!)/(2! 2!) = 15`

case 5 when three are of same type and 2 are of different color = 1

total number of distinct combination is 82