Q. 275.0( 1 Vote )
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
Answer :
Given that we need to select 11 players out of available 17 players in which 5 players are bowlers.
It is also mentioned that each team should contain exactly 4 bowlers.
Let us assume the no. of ways of selection be N.
⇒ N = (no. of ways of selecting 4 bowlers out of 5) × (no. of ways of selecting 7 players from remaining 12 players)
⇒ N = (5C4) × (12C7)
We know that 
,
And also n! = (n)(n – 1)......2.1
⇒ 
⇒ 
⇒ 
⇒ N = 5 × 792
⇒ N = 3960
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