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?

Asked by Pragya Singh | 1 year ago |  66

##### Solution :-

Given 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers

There are 5 players how bowl, and we can require 4 bowlers in a team of 11

Number of ways in which bowlers can be selected are: 5C4

Now other players left are = 17 – 5(bowlers) = 12

Since we need 11 players in a team and already 4 bowlers are selected, we need to select 7 more players from 12.

Number of ways we can select these players are: 12C7

Total number of combinations possible are: 5C4 × 12C7

5C4 × 12C7 $$\dfrac{5!}{4!(5-4)!}\times \dfrac{12!}{7!(12-7)!}$$

$$\dfrac{5!}{4!\times 1!}\times \dfrac{12!}{7!\times 5!}$$

5C4 × 12C7 = $$\dfrac{5\times 4!}{1!\times 4!}\times \dfrac{12\times 11\times 10\times 9\times 8\times 7!}{5!\times 7!}$$

$$\dfrac{5}{1}\times \dfrac{95040}{120}$$

$$5\times 792=3960$$

Number of ways we can select a team of 11 players where 4 players are bowlers from 17 players are 3960

Answered by Abhisek | 1 year ago

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