Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if
(a) a student can receive any number of awards?
(b) each student can receive at most 1 award?
We have 30 to choose from for the first award, and 30 for the next and so on....
We have 30 to choose from for the first award, and then 29 for the next and so on...
$$30 \cdot 29 \cdot 28 \cdot 27 \cdot 26 =17100720$$
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