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Grade: 11
        
Number of ways to distribute n distinct  items into r distinct bins (r
8 months ago

Answers : (2)

Arun
22340 Points
							
For n distinct objects into r distinct groups:
 
  1. Number of ways exactly 1 object can be placed in r groups = nCr
  2. Number of remaining objects = (n-r)
  3. Now, each of these (n-r) objects can be placed into any of the r groups.
  4. Hence, number of ways of distributing them = (n-r)^r
  5. Therefore, total number of ways of doing this =  nCr * (n-r)^r

Answer : nCr * (n-r)^r
8 months ago
Natarajan
22 Points
							
Arun,
Thank you so much for your quick response. This is a very good way of thinking. Really appreciate. However. I have a doubt. nCr is the number of ways of selecting r items from n items. But they can be put in r bins in r! ways. Then each of the (n-r) items can be placed in r bins in (n-r)^r ways. So the total number of ways should be nCr.*r! * (n-r)^r. Appreciate your comments
8 months ago
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