Question

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 1

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,

ⁿC_r = \(\frac{n!}{(n-r)!r!}\)

And also,

n! = (n)(n – 1)......2.1

⇒ N = 5 × 792 

⇒ N = 3960