Question

Mrs lunette has 18 students in her class. She wants to send 3 of these students to pick up book for the class. How many combinations of 3 students can she choose?

Answer 1

Mrs Lunette can choose 816 combinations of 3 students.

Explanation:

We can use the combination formula to find the number of combinations Mrs Lunette has,

Number of combinations =
`(n!)/(k!(n-k)!)`

Where,

`n` is the total number of students.

`k` is how many students can be chosen at a time.

Now we can substitute the values to the above equation,

Number of combinations =
`(18!)/(3!(18-3)!)`

=
`(18!)/(3!(15)!)`

=
`(18*17*16)/(3!)`

=
`(18*17*16)/(3*2*1)`

=
`(3*17*16)/(1)`

=
`816`

Mrs Lunette can choose 816 combinations of 3 students.