A nine-member committee of an Agricultural University consists of 4 B. Tech., 3 M. Tech., and 2 Ph. D. students. It is decided to remove three students from the committee at random. The probability of removing 2 students from the same category and the third one from any other category is ______. [round off to 3 decimal places]
Official Answer Key:
0.654 to 0.656
Step-by-Step Solution & Explanation
Total ways to choose 3 of 9 = C(9,3) = 84. Favourable outcomes (2 from one category + 1 from a different category): 2 B.Tech & 1 other = C(4,2)×C(5,1) = 6×5 = 30; 2 M.Tech & 1 other = C(3,2)×C(6,1) = 3×6 = 18; 2 Ph.D & 1 other = C(2,2)×C(7,1) = 1×7 = 7. Total favourable = 30+18+7 = 55. Probability = 55/84 = 0.6548.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.