Question #f07f8

1 Answer
Aug 3, 2017

Answer:

#(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#