SOLUTION: Five separate awards are to be presented to selected students from a class of size 30. a) How many different outcomes are possible if a student can receive any number of awards

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Question 561438: Five separate awards are to be presented to selected students from a class of size 30.
a) How many different outcomes are possible if a student can receive any number of awards?
b) How many different outcomes are possible if each student can receive at most one award?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Five separate awards are to be presented to selected students from a class of size 30.
a) How many different outcomes are possible if a student can receive any number of awards?:::
The 1st student may or may not receive each of the 5 awards: 2^5 = 32 ways
The 2nd student the same: 32 ways
The 3rd student the sam: 32 ways
Total # of ways = 32^3 = 32768
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b) How many different outcomes are possible if each student can receive at most one award?
1st student 5
2nd student 4
3rd student 3
Total 5*4*3 = 60 ways
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Cheers,
Stan H.