Question

The chess club has 18 students. How many different teams of 4 can be formed for competition?
3,060
18,360
73,440

Answer 1

Number of students in chess club = 18
Number of students in a team = 4
so, number of teams can be formed for competition = ¹⁸C₄
= 18!/(18 - 4)! × 4!
= 18!/14! × 4!
= 18 × 17 × 16 × 15 × 14!/{14! × 4 × 3 × 2 × 1}
= 18 × 17 × 16 × 15/24
= 3 × 17 × 16 × 15/4
= 3 × 17 × 4 × 15
= 51 × 60
= 3060

Hence, answer is 3060

Answer 2

Given, no. of students in chess club = 18

Number of students in the required team = 4

No. of teams that can be made = ¹⁸C₄

So, we solve and get

= 18!/(18 - 4)! × 4!

= 18 × 17 × 16 × 15 × 14!/{14! × 4 × 3 × 2 × 1}

= 18 × 17 × 16 × 15/24

= 3 × 17 × 4 × 15

= 3060