# 5 Students Selected Part Three (final part)

##### New member
5 students selected from class of 42. How many selections possible if 5 are selected and each student gets an A. You can only receive one grade. I feel like this one, as its predecessors, is devilishly simple. Is this another case of 42 to the fifth, perhaps? I thank you immensely.

#### soroban

##### Elite Member

5 students selected from class of 42 and given an A.
How many selections are possible if you can only receive one grade.

I feel like this one, as its predecessors, is devilishly simple.
Is this another case of 42 to the fifth, perhaps? . . . . no

This time 5 students are selected from the class of 42,
. . but they all receive the same grade.
Their order is not considered.

This is a Combination problem.
The number of ways is: .$$\displaystyle _{42}C_5 \:=\:\dfrac{42!}{5!\,37!} \:=\:850,\!668$$