A team of 3 tennis players is to be finalized from a group of 2 male and 3 female. In how many ways this can be done and how many teams which consist of 1 male and 2 female?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10 and 6
A team is a selection, not an arrangement, so the order of the players does not matter and combinations are used: \(^{n}C_{r}\) is the number of ways to choose \(r\) from \(n\).
Any 3 of the 5 players (2 male + 3 female): \(\displaystyle ^{5}C_{3}=\frac{5\times4\times3}{3\times2\times1}=10\)
1 male out of 2 and 2 females out of 3: \(^{2}C_{1}\times{}^{3}C_{2}=2\times3=6\)