JCCDQBHWHCB007(i) Combinatorics : Choosing with special conditions

     This sort of question has appeared in the GCE ‘A’ levels before.  For questions with special conditions, a good approach is to consider to the special conditions first.

Suggested Approach and Solution:-

 

Number of ways to choose the young player = ²C₁ = 2

The captain must be in, so two vacancies have been taken up and there are 3 left.  These places must be filled from the 7 eligible other players (excluding the captain and the two youngest players).  There are   ⁷C₃ = 35  ways to do this.  The total number of ways is

          35 x 2 = 70