Question

The WNBA champions have a twelve-player roster that includes two superstars. If a group of five starting players for this team must include the two superstars, how many different groups of five starting players are there?

Answer 1

120 groups

Explanation:

Total number of players = 12

Number of superstars = 2

To select a group of 5 players that MUST include the two superstars can be done in how many different ways?

Since the two superstars must always be in the 5 player team

Number of players left to choose = 5 - 2 = 3

Number of players from which selection is to be made = 12 - 2 = 10

Hence, the number of ways of choosing 3 players from 10 ; 10C3

Recall ;

nCr = n! / (n-r)!r!

10C3 = 10! ÷ (10-3)!3!

10C3 = 10! ÷ 7!3!

10C3 = (10*9*8) / (3*2*1)

10C3 = 720 / 6

10C3 = 120 groups