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This question already has an answer here:

I have a question about the basic counting problem.

Situation : There are 50 people and 10 chairs in the room. Among them, 5 chairs are already assigned the special 5 people of the 50 people. In this situation, how many ways can the 10 chairs be distributed? (each chair is not distinguishable)

My answer : I thought that 45 x 44 x 43 x 42 x 41, since 5 chairs are already assigned. So, except for 5 people who have their chairs, among 45 people, we can distribute the left 5 chairs to them.

Is this correct?

Any comments would be helpful to me. Thanks.

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marked as duplicate by 6005, Henry Swanson, Joey Zou, Gabriel Romon, Parcly Taxel Aug 31 '16 at 6:36

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ If the chairs are not distinguishable, you need to divide that number by 5!. This is same as choosing 5 people from 45 people. $\endgroup$ – user348749 Aug 31 '16 at 0:09
  • $\begingroup$ I see. But, I'm so confused of this question because of the special 5 people. Could you give me any explanation how to deal with the special 5 people in this problem? $\endgroup$ – baek Aug 31 '16 at 0:18
  • $\begingroup$ Since the special people are already assigned and the chairs are not distinguishable, they need not be counted. We need to choose 5 people for the other chairs only. $\endgroup$ – user348749 Aug 31 '16 at 0:19