Multiple choice

An urn contains 6 different black balls and 4 different blue balls. In how many ways can 6 balls be selected so that there are at least two balls of each colour?

  1. 185 ways

  2. 120 ways

  3. 125 ways

  4. 124 ways

  5. 123 ways

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total ways to select 6 balls from 10 is 10C6 = 210. We need at least two of each color. Possible combinations: (2B, 4b) or (3B, 3b) or (4B, 2b). 6C2*4C4 + 6C3*4C3 + 6C4*4C2 = (15*1) + (20*4) + (15*6) = 15 + 80 + 90 = 185.