Question

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?

Answer 1

Given as

The number of players = 15

The number of players to be selected = 11

On using the formula,

ⁿC_r = n!/r!(n – r)!

¹⁵C₁₁ = 15! / 11! (15 – 11)!

= 15! / (11! 4!)

= [15 × 14 × 13 × 12 × 11!] / (11! 4!)

= [15 × 14 × 13 × 12] / (4 × 3 × 2 × 1)

= 15 × 7 × 13

= 1365

Therefore, total number of ways of choosing 11 players out of 15 is 1365 ways.