Permutations or Combinations?

ms. confused

In how many ways can 15 gifts be distributed equally:

a) amongst Claire, Alana, and Kalena

b) into three parcels of five gifts each

For (a) I went $$_{15} P_{3}/3 = 910$$

I am 100% certain this is wrong. I also have no idea how to do (b). I would greatly appreciate any help on this question. Related Introductory Physics Homework Help News on Phys.org

HallsofIvy

Homework Helper
Is order important? That is, does it matter which was the first present or is it just a matter of who get what present. If order is important, then it is a permutation problem. If not, then it is a combination problem.

geosonel

ms. confused said:
In how many ways can 15 gifts be distributed equally:

a) amongst Claire, Alana, and Kalena

b) into three parcels of five gifts each

For (a) I went $$_{15} P_{3}/3 = 910$$

I am 100% certain this is wrong. I also have no idea how to do (b). I would greatly appreciate any help on this question. a) from the 15 gifts, first choose 5 from the 15 for Claire, then 5 from the remaining 10 for Alana, and then 5 from the remaining 5 for Kalena. number ways would then be (since order within each choosing of 5 does not matter):
$$\mathbb{C}_{5}^{15} \cdot \mathbb{C}_{5}^{10} \cdot \mathbb{C}_{5}^{5} \ = \ (3003) \cdot (252) \cdot (1)$$
b) solution would be similar except order of choosing 1st for Claire, 2nd for Alana, & 3rd from Kalena no longer matters. (of course, the choosing order of the 5 within each group still does not matter). so just divide answer (a) by (3!) to remove the ordering among Claire, Alana, & Kalena to produce 3 parcels of 5 gifts each.

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