Distributing Presents Among Children

  • Thread starter squaremeplz
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In summary, the total number of ways to distribute 15 identical gifts between 10 distinct children is the sum of the binomial coefficients (15 0) + (15 1) + (15 2) + ... + (15 10), where each coefficient is calculated using the formula n!/[(n-k)!k!]. This approach takes into account all possible combinations of gifts being given to each child, resulting in a total of 3003 ways.
  • #1
squaremeplz
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Homework Statement



in how many ways can one distribute 15 identical gifts between 10 distinct children?


Homework Equations



(n + k - 1, k - 1) bionomail coeff.

The Attempt at a Solution



n = 15, k = 10

(24, 9) = 24!/(9!*15!)

It would be much appreciated if someone can verify my result. Thanks.
 
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  • #2
I don't think what you have is right. I think the total number of ways is the sum of the binomial coefficients
(15 0) + (15 1) + (15 2) + ... + (15 10) where each one is n!/[(n - k)! k!]

My reasoning is this:
(15 0) - the number of ways to give all 15 gifts to no one--1 way
(15 1) - the number of ways to give all 15 gifts to 1 child--15 ways
(15 2) - the number of ways to give 15 gifts to 2 children (and hence none to the other 8)
And so on.
Anyway, that's how I would approach this problem.
 

What is the best way to distribute presents?

The best way to distribute presents depends on the specific situation and the preferences of the individuals involved. Some common options include handing out presents one at a time, having a gift exchange game, or using a secret Santa system.

How can I ensure fairness when distributing presents?

To ensure fairness, it is important to establish clear rules and guidelines for how presents will be distributed. This could include setting a budget for gifts, using a random selection method, or having a designated person oversee the distribution process.

What should I do if someone receives a present they don't like?

If someone receives a present they don't like, it is important to be respectful and gracious. They can politely thank the gift-giver and, if appropriate, consider exchanging the gift or regifting it to someone else.

How can I make distributing presents more efficient?

To make distributing presents more efficient, consider organizing a gift exchange where each person brings one gift and everyone takes turns choosing a present. This can save time and ensure everyone receives a gift they like.

Are there any cultural considerations to keep in mind when distributing presents?

Yes, it is important to be aware of cultural differences and customs when distributing presents. For example, some cultures may have specific rules about gift-giving or may place more emphasis on group gifts rather than individual presents.

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