Permutation

[Ruben]

Hi,

Can someone help?

Thanks

There are four contestants in the competition for 6 different prizes. Each contestant can win one prize. How many different outcomes are possible at the competition for the four contestants?

A) 15

B) 30

C) 60

D) 180

E) 360

[dbernst]

Ruben, one key to correctly answering a combinatorics problem is to identify the problem type as an arrangement (permutation) or a grouping (combination). This is simply a relatively straightforward arrangement problem.

The first contestant to win a prize has 6 potential outcomes. As this person must win one prize (no matter which prize it is), the second contestant has 5 potential outcomes. By the same logic, the third contestant has 4 potential outcomes, and the fourth contestant has 3 potential outcomes.

The total number of arrangements (permutations) is simply the product of the number of outcomes for each contestant:
6*5*4*3 = 360.

The correct answer is E.

ps. You might see other notation or approaches concerning these types of combinatorics problems (such as 6P4 or 6!/2!) but the underlying logic is identical.

Hope that helps.
-dan

[mpavey]

The way I read this question, it is ambiguous. It sounds like it would be possible for each contestant to win more than one prize. That would mean that contestant 1 could walk away with no prizes, one prize, two prizes, ... or even all six prizes.

How would we calculate the number of possible outcomes in this case?

[StaceyKoprince]

"Each contestant can win one prize" is not ambiguous. Each can win one prize, period.

You won't see a question of the type you describe on the test because it would take longer than 2 minutes to calculate (without a calculator).