A box contains 4 white balls, 5 black balls and 6 red balls. In how many ways can four balls be drawn from the box if at least one ball of each colour is to be drawn (if balls of same colour are diffe

Question

A box contains 4 white balls, 5 black balls and 6 red balls. In how many ways can four balls be drawn from the box if at least one ball of each colour is to be drawn (if balls of same colour are different)

TestHub · Accepted Answer

Four balls with at least one of each colour means the split is 2-1-1 by colour: 4 C 2 ​ 5 C 1 ​ 6 C 1 ​ + 4 C 1 ​ 5 C 2 ​ 6 C 1 ​ + 4 C 1 ​ 5 C 1 ​ 6 C 2 ​ = 180 + 240 + 300 = 720 Also 2 1 ​ 4 C 1 ​ 5 C 1 ​ 6 C 1 ​ 12 C 1 ​ = 2 4 ⋅ 5 ⋅ 6 ⋅ 12 ​ = 720

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