In how many ways can a team of 11 cricket players be chosen from 14 players?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 364
A team is a selection: the order in which the players are picked does not matter, so the number of ways is \({}^{14}C_{11}\). Choosing the 11 who play is the same as choosing the 3 who are left out, so \({}^{14}C_{11}={}^{14}C_{3}\), which is quicker to work out.
Ways of choosing the 3 players left out: \(\displaystyle {}^{14}C_{3}=\frac{14\times13\times12}{3\times2\times1}\)
This gives \(14\times13\times2=364\) ways