Question

How many ways can a dance instructor send 4 of her 11 students to a summer dance program?

7920




1980




720




330

Answer 1

d) 330

Explanation:

The number of ways can a dance instructor send 4 of her 11 students to summer dance program is C(11 , 4)

That is
`11_{C_(4) }` ways

by using formula
`n_{C_(r) } = (n!)/((n-r)!r!)`

now simplification

`11_{C_(4) } = (11!)/((11-4)!4!)`

=
`(11X10X9X8X7!)/((7!)4X3X2X1)`

after cancelling 7! and on simplification

=
`(11X10X9X8)/(4X3X2X1)`

after cancellation we get 330 ways

The number of ways can a dance instructor send 4 of her 11 students to summer dance program is 330