Question

Which two terms represent the number of groups of three players that are all juniors?

3,003
20
14^C^3
14^C^6
6^C^3
364

Answer 1

We shall use combination here

• n=6
• r=3

`\boxed{\sf ^nC_r=(n!)/(r!(n-r)!)}`

Now

`\\ \rm\Rrightarrow ^6C_3`

`\\ \rm\Rrightarrow (6!)/(3!(6-3)!)`

`\\ \rm\Rrightarrow (720)/(3!(6))`

`\\ \rm\Rrightarrow 20`

Answer 2

• B) 20, E) 6C3

Explanation:

Combination of 3 juniors out of 6 is:

• 6C3 = 6!/(6 - 3)!3! = 6*5*4*3!/3!3! = 6*5*4/2*3 = 5*4 = 20

Correct choices are B and E