Doling out the prizes

Probability Level 1

There are 20 distinct people signed up for a raffle. There are 3 prizes that can be won: a 100 cm HDTV, a signed football jersey, and an envelope filled with gift cards. It is possible for a person to win more than one prize.

How many possible prize distributions are there?


The answer is 8000.

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Andy Hayes by Andy Hayes , 38, USA

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3 solutions

Andy Hayes
May 10, 2016

Relevant wiki: Rule of Product - Basic

This problem can be modeled as 3 3 distinct objects being distributed into 20 20 distinct bins. Using the formula for distinct objects into distinct bins, there are 2 0 3 = 8000 20^3=\boxed{8000} possible distributions of these objects.

15 Helpful 0 Interesting 0 Brilliant 3 Confused
Thabo Lekgetho
Apr 21, 2017

8000 bold text

0 Helpful 0 Interesting 0 Brilliant 0 Confused

At least you wrote Bold Text in Bold Fonts .

Akash Tyagi - 2 years, 1 month ago
Nandni Jotwani
Jul 13, 2016

I agree with Andy's solution I did it in the same way

0 Helpful 0 Interesting 0 Brilliant 0 Confused

here make a function mapping. 3 prizes go into the domain set and 20 distinct people in Codomain.as one prize can't be distributed among more than one people.so the number of function could be made or the number of distribution of prizes are (codomain)^domain or 20^3 or 8000

Ashik Shahriar - 1 year ago

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