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Permutations or Combinations?

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 [tex]_{15} P_{3}/3 = 910[/tex]

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. :cry:
 

HallsofIvy

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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.
 
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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 [tex]_{15} P_{3}/3 = 910[/tex]

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. :cry:
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):
[tex] \mathbb{C}_{5}^{15} \cdot \mathbb{C}_{5}^{10} \cdot \mathbb{C}_{5}^{5} \ = \ (3003) \cdot (252) \cdot (1) [/tex]
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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