Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30

# Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30

J
240 points

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?

Five separate
jeffp

8.7k points

part (a)

We have 30 to choose from for the first award, and 30 for the next and so on....

$$30^5=24300000$$

part (b)

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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