Lakshman Patel RJIT
asked
in Quantitative Aptitude
Mar 31, 2020
recategorized
Sep 11, 2020
by Lakshman Patel RJIT

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1 vote

A college cricket team with $11$ players consists of $4$ batsman, $3$ all-rounders, $3$ bowlers and $1$ wicket keeper. $3$ players are selected randomly. Find the probability that the selection contains a batsman, a bowler and an all-rounder.

- $\dfrac{12}{60} \\$
- $\dfrac{13}{25} \\$
- $\dfrac{12}{55} \\$
- $\dfrac{104}{165}$

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Best answer

$11$ players$:4$ batsman, $3$ all-rounders, $3$ bowlers and $1$ wicket keeper.

$3$ players are selected randomly $\implies ^{11}C_{3} = \dfrac{11!}{8!3!} = \dfrac{11\cdot 10\cdot 9\cdot 8!}{8!\cdot 3\cdot 2\cdot 1} = 165$

The selection contains a batsman, a bowler and an all-rounder $\implies ^{4}C_{1} \times ^{3}C_{1} \times ^{3}C_{1} = 36$

Probability of an event happening $ = \dfrac{\text{Number of ways it can happen}}{\text{Total number of outcomes}} = \dfrac{36}{165}=\dfrac{12}{55}.$

So, the correct answer is C.

$3$ players are selected randomly $\implies ^{11}C_{3} = \dfrac{11!}{8!3!} = \dfrac{11\cdot 10\cdot 9\cdot 8!}{8!\cdot 3\cdot 2\cdot 1} = 165$

The selection contains a batsman, a bowler and an all-rounder $\implies ^{4}C_{1} \times ^{3}C_{1} \times ^{3}C_{1} = 36$

Probability of an event happening $ = \dfrac{\text{Number of ways it can happen}}{\text{Total number of outcomes}} = \dfrac{36}{165}=\dfrac{12}{55}.$

So, the correct answer is C.