Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
(With fixed number of objects in each group)
(i) Into groups of unequal size (different number of objects in each group)
(a) Number of ways, in which n distinct objects can be divided into r unequal groups containing a1, a2, a3, ......, ar things (a1 ≠ aj)
= nCa1. n-a1Ca2. n-a1-a2Car. = n!/a1!a2!a3!...ar!
Here a1 + a2 + a3 + ...... + ar = n.
(b) Number of ways in which n distinct objects can be distributed among r persons such that some person get a1 objects,
another person get a2 objects ......... and similarly someone gets ar objects = n!r! /a1!a2!a3!...ar!.
Explanation: Let us divide the task into two parts. In the first part, we divide the objects into groups. In the second part, these r groups can be assigned to r persons in r! ways.
(ii) Into groups of equal size (each group containing same number of objects)
(a) Number of ways in which m × n distinct objects can be divided equally into n groups (unmarked) = (mn)!/(m!)n n!.
(b) Number of ways in which m × n different object can be distributed equally among n persons (or numbered groups)
= (number of ways of dividing) × (number of groups)! = (mn)!n!/(m!)n n! = (mn)!/(m!)n .
IIT JEE study material is available online free of cost at askIITians.com. Study Physics, Chemistry and Mathematics at askIITians website and be a winner. We offer numerous live online courses as well for live online IIT JEE preparation - you do not need to travel anywhere any longer - just sit at your home and study for IIT JEE live online with askIITians.com.
To read more, Buy study materials of Permutations and Combinations comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Restricted Selection and Arrangement (a) The...
Combinations Table of Content What do you mean by...
Circular Permutations The arrangements we have...
Derangement Theorem and Multinomial Theorem Table...
Useful Tips for Algebra Some Useful Tips (i)...
Permutations Vs Combinations Difference between...
Permutaions and Combinations – Solved...
Fundamental Principle of Counting Table of Content...
Permutations Table of Content What do you mean by...