0

Guest

Courses New

Number of ways to distribute n distinct items into r distinct bins (r

Number of ways to distribute n distinct  items into r distinct bins (r

Grade:11

2 Answers

Arun
25750 Points
5 years ago
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
Natarajan
22 Points
5 years ago
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

Think You Can Provide A Better Answer ?

Other Related Questions on IIT JEE Entrance Exam

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More