A bag contains 5 green balls, 4 yellow balls, and 3 red balls. Three balls are drawn one after another without replacement. What is the probability that all three balls drawn are of different colours?
(A) 3/22
(B) 5/24
(C) 3/11
(D) 4/27

Question

A bag contains 5 green balls, 4 yellow balls, and 3 red balls. Three balls are drawn one after another without replacement. What is the probability that all three balls drawn are of different colours?
(A) 3/22
(B) 5/24
(C) 3/11
(D) 4/27

ONLiNE UPSC · Accepted Answer

Total balls: 5 (green) + 4 (yellow) + 3 (red) = 12 balls
Ways to pick 3 balls:
12C3 = 220
Ways to pick one of each colour:
Choose 1 green: 5 ways
Choose 1 yellow: 4 ways
Choose 1 red: 3 ways
Total = 5 &times; 4 &times; 3 = 60
Required, Probability: 60/220 = 3/11

Hence, option c is correct.

Probability

Probability of drawing balls of different colors

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M Question 1	⏱ 0
A bag contains 5 green balls, 4 yellow balls, and 3 red balls. Three balls are drawn one after another without replacement. What is the probability that all three balls drawn are of different colours? (A) 3/22 (B) 5/24 (C) 3/11 (D) 4/27