Question

GUYS PLEASE HELP MEEE

There are 20 members in a badminton club. The club coach wants to select two members of the same gender to represent the club in a doubles game. There are 99 possible choices. If the club has more female than male members, how many female members are there?

OPTION :

A. 13
B. 11
C. 15
D. 17​

Answer 1

A. 13

Explanation:

Let x be the number of female members.

There are x!/(x - 2)!2! ways to choose the female team

There are (20 - x)! / (20 - x - 2)!2! = (20 - x)! / (18 - x)!2! ways to choose the male team.

x!/(x - 2)!2! + (20 - x)! / (18 - x)!2! = 99

As I'm terrible at factorial algebra, and we only have four options, let's just plug some in.

11! / 9!2! + 9! / 7!2! = 55 + 36 = 91 Nope

13! / 11!2! + 7! / 5!2! = 78 + 21 = 99 WINNER

15!/13!2! = 105 Nope, don't even bother counting the boys.

17!/15!/2! = 136 Nope