Answer:
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 - [tex]^7C_5 = 21[/tex]
case - 2 when there is 3 different color and two are of same color [tex]^6C3_ \times 2 = 30[/tex]
case 3 - when 2 are of different type and 3 are of same color[tex]= ^6C2_ = 15[/tex]
case 4 - when 1 are of different color and 2 are of different color[tex] =^5C1_ \times \frac{4!}{2! 2!} = 15[/tex]
case 5 when three are of same type and 2 are of different color = 1
total number of distinct combination is 82
