Aptitude Overflow
0 votes
92 views

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.

  1. $\dfrac{12}{60} \\$
  2. $\dfrac{13}{25} \\$
  3. $\dfrac{12}{55} \\$
  4. $\dfrac{104}{165}$
in Quantitative Aptitude by (5.8k points) 5 56 296
recategorized by | 92 views

1 Answer

0 votes
$11$ 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}.$

So, the correct answer is _______
by (5.8k points) 5 56 296
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
4,624 questions
1,789 answers
541 comments
44,737 users