Grade Upto college levelDiscuss with colleagues and IITians
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
1 Answer
Arun
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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