Abag 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

total number of distinct combination is 82

Step-by-step 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 -

case - 2  when there is 3 different color and two are of same color

case 3 - when 2 are of different type and 3 are of same color

case 4 -  when 1 are of different color and 2 are of different color

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

total number of distinct combination is 82