QR permutation/combination problems

[299678]

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How many ways can we give 3 prizes to two student, when both of them are equally eligible for all the prizes?

 

[Streetwolf]

How many ways can we give 3 prizes to two student, when both of them are equally eligible for all the prizes?

Do each of them only get 1 prize?

If so this is a simple (3 P 2) problem. You are picking out the two prizes that the students will receive. Order matters.

This equals 6 ways.

 

[299678]

Yeah that's what I got, but the correct answer is 4

 

[Streetwolf]

Yeah that's what I got, but the correct answer is 4

Maybe they wanted:

(0, 3)
(1, 2)
(2, 1)
(3, 0)

Where (1,2) means student A got 1 prize and student B got 2 prizes.

But that doesn't account for specific prizes in the (1,2) and (2,1) cases.



If each student HAD to get a prize then only (1,2) and (2,1) are possible.

In that case you have 3 choices for each though and it would STILL be 6 ways.


Problem could be asking for something different.


Or they have the wrong answer listed.