Question 7 In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Class X1 - Maths -Permutations and Combinations Page 153
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in a cricket team , there are 17 players . in which 5 bowler and 12 Batsmen.
we have to select 11 players including exactly 4 bowlers .
so, 4 bowlers will be selected from 5 bowlers. and remaining 7 players will be selected from 12 Batsmen .
hence, total number of ways for selecting exactly 4 bowlers = ⁵C₄
total number of ways for selecting 7 batsmen = ¹²C₇
a/c to fundamental principal of counting,
total number of ways of selecting 11 players = ⁵C₄ × ¹²C₇
= 5!/4! × 12!/7!×5!
= 12 × 11 × 10 × 9 × 8/24
= 3960 ways
we have to select 11 players including exactly 4 bowlers .
so, 4 bowlers will be selected from 5 bowlers. and remaining 7 players will be selected from 12 Batsmen .
hence, total number of ways for selecting exactly 4 bowlers = ⁵C₄
total number of ways for selecting 7 batsmen = ¹²C₇
a/c to fundamental principal of counting,
total number of ways of selecting 11 players = ⁵C₄ × ¹²C₇
= 5!/4! × 12!/7!×5!
= 12 × 11 × 10 × 9 × 8/24
= 3960 ways
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