Question

Exercise 1.6. There are 10 red jelly beans, 8 blue jelly beans and 12 green jelly beans in a jar.
1. How many ways could I pick out any combination of three jelly beans?

2. If I pick out three jelly beans, in how many ways could I pick exactly two red or exactly two green jelly beans?

3. If I pick out three jelly beans, in how many ways could I pick exactly one blue jelly bean?

Answer 1

Given  There are 10 red jelly beans, 8 blue jelly beans and 12 green jelly beans in a jar

total number of jelly beans = 10 + 8 +12 = 30

1) How many ways could I pick out any combination of three jelly beans?

any combination means we have to pick 3 out of 30, hence the number of ways = ³⁰C₃ = 4060

2) If I pick out three jelly beans, in how many ways could I pick exactly two red or exactly two green jelly beans?

Lets say initially we pick two red

number of ways of selecting 3 balls with exactly 2 red balls = ¹⁰C₂ * ²⁰C₁ = 900

Lets say initially we pick two green  

number of ways of selecting 3 balls with exactly 2 green balls = ¹²C₂ * ¹⁸C₁ = 1188

total number of ways = 900 + 1188 = 2088

3) If I pick out three jelly beans, in how many ways could I pick exactly one blue jelly bean

one from 8 blue and other two from 22 jelly

= ⁸C₁* ²²C₂ = 1848