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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.


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

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  • $\begingroup$ 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