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how many ways we can divide mn members into 1.m groups2.m persons

how many ways we can divide mn members into 1.m groups2.m persons

Grade:Upto college level

1 Answers

Arun
25750 Points
3 years ago
Let us understand this by considering  
′
 mn 
′
  number of alphabets, of which  
′
 n 
′
  number of groups exist.
∴ No. of alphabets in each group
= 
n
mn
​ 
 =m
Now, if there are  
′
 mn 
′
  number of alphabets, of which  
′
 m 
′
  alphabets are identical and such identical groups are  
′
 n 
′
 , then number of arrangements of these alphabets = 
m!×m!×m!....n(times)
(mn)!
​ 
 
= 
(m!) 
n
 
(mn)!
​ 
 
 
So, this is the number of distribution of  
′
 mn 
′
  things into  
′
 n 
′
  equal groups.
Now, division is just the number of selection and not the arrangements.
∴ No. of ways of dividing = 
(m!) 
n
 n!
(mn

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