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How many different ways can 200 coins be distributed among 10 people so that:

1)everyone gets 0, or more, coins?

2)everyone gets 5, or more, coins?

I know how to do question it they have an exact requirement like if they each need a certain amount. However, when it comes to 0 or more I don't know how to approach the question can someone teach me the way? Thank you.

Tony
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  • The correct search term here is stars and bars. Also, if ten people get 5 or more coins each., that would require at least 50 coins to cover the minimums for everyone... which is more than 40 so... – JMoravitz Sep 20 '19 at 21:56
  • Sorry man I got the question wrong is there a way of how to tackle the question now? – Tony Sep 20 '19 at 22:00
  • Again, I refer you to the link I gave. It very clearly outlines how to approach problems like these and gives proofs for the formulas. The only thing remaining for the second problem is to recognize that to distribute $200$ coins to $10$ people where each gets at least five, you can first give everyone five coins and then the question becomes how many ways you can distribute the remaining $150$ coins among $10$ people such that they each get $0$ or more. – JMoravitz Sep 20 '19 at 22:01
  • Alright, Thankyou man it means a lot. – Tony Sep 20 '19 at 22:04

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