# 5 Students Selected

Here it is:Suppose 5 students are randomly selected in a class of 42. How many selections are possible if 5 students are selected with the first winning $100, second$75, third $50, fourth$25, fifth $10. A student can win more than one.I don't even know where to start. Permutations? Combination? I feel like this has multiple steps, but of what I do not know. Thanks! #### soroban ##### Elite Member Hello, SadAtMath! Evidently, you are over-thinking the problem. Suppose 5 students are randomly selected in a class of 42. How many selections are possible if 5 students are selected with the first winning$100, second $75, third$50, fourth $25, fifth$10.
A student can win more than one prize.

I don't even know where to start. Permutations? Combination?
I feel like this has multiple steps, but of what I do not know. Thanks!

There are 42 choices for the winner of the 1st prize.
There are 42 choices for the winner of the 2nd prize.
There are 42 choices for the winner of the 3rd prize.
There are 42 choices for the winner of the 4th prize.
There are 42 choices for the winner of the 5th prize.

Get it?

There are: .$$\displaystyle 42^5 \:=\:130,\!691,\!232$$ possible selections.