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