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Byju's Answer
Standard VII
Mathematics
Integers
Using permuta...
Question
Using permutation or otherwise prove that
n
2
!
(
n
!
)
n
is an integer, where n is a positive integer.
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Solution
We have
n
2
people, to be divided into
n
teams, each of which has
n
people.
Line up the
n
2
people, put the first
n
into a team, then the next
n
, and the next, and so on.
The no. of ways
n
2
people can be divided into
n
trams
(
n
2
)
!
(
n
!
)
n
No. of ways is always on integer.
Therefore
(
n
2
)
!
(
n
!
)
n
is an integers
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