Question

Question #f07f8

Answer 1

`(30!)/(6!(30-6)! ) = 593,775`

Explanation:

`20%` of the students will be evaluated. The order in which the teacher sees them is not important, as long as `6` of them are chosen.

There are `30` choices for the first student, then `29` for the second, then `28` and so on until `6` students are chosen.

The total number of possible groups of `6` is

`30xx29xx28xx27xx26xx25`

This can also be written as `(30!)/((30-6)!)`

`(30*29*28*27*26*25cancel(*24*23*22 ...).)/cancel(24*23*22*...)`

However within this number of groups, the same groups just in a different order are included, so we need to reduce the number by the number of ways of arranging `6` students which is `6!`

The number of different groups of `6` students is:

`(30!)/(6!(30-6)! ) = 593,775`