In a cohort of thirty graduating students, there are three different prizes to be awarded. If...
In a cohort of thirty graduating students, there are three different prizes to be awarded. If no student can receive more than one prize, in how many different ways could the prizes be awarded?
Homework Answers
The first prize may be awarded in any of 30 ways: any student may get it.
After the first prize has been awarded, the second prize may be awarded to any of the 29 students who have not yet won the price.
After both the prize is awarded, the third prize may be awarded to any one of the 28 remaining students who have not won either of the other two prizes.
Since all three prizes are awarded, we multiply the total possibilities:
30×29×28 = 24360
In 24360 different ways the prizes are awarded.
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