Question
A junior baseball team consists of six boys and three girls. The team members are to be placed in a line to have their photograph taken.
(a) In how many ways can the team members be placed if
(i) there are no restrictions; [1]
(ii) the girls must be placed next to each other. [2]
(b) Five members of the team are selected to attend a baseball summer camp. Find the number of possible selections that contain at least two girls. [3]
▶️Answer/Explanation
(a)(i) \[ 9! = 362880 \]
(a)(ii) Treat the three girls as a single entity: \[ 3! \times 7! = 30240 \]
(b) The number of ways to select at least two girls: \[ \binom{3}{2} \times \binom{6}{3} + \binom{3}{3} \times \binom{6}{2} = 60 + 15 = 75 \]