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?

Solution:

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ⁿCᵣ = n! / [r!(n−r)!]. Using this,

• No. of ways in which 4 bowlers can be selected from 5 bowlers = ⁵C₄.
• No. of ways in which 7 players can be selected from the remaining 12 players = ¹²C₇.

By fundamental principle of counting,

Total number of ways = ⁵C₄ × ¹²C₇

= (5!) / [4! (5-4)!] × (12!) / [7! (12-7)!]  (Using nCr formula)

= 5 × 792

= 3960

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 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?

Summary:

The number of ways in which one can 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 is 3960