Let 
. Let 
be the number of 9 -digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let 
be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
Text Solution
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counts 9 -digit numbers using 
with exactly one digit repeated twice (8 distinct digits, one twice, one absent).
Choose digit appearing twice: 9 ways.
Choose absent digit: 8 ways.
Arrange: 
ways.
.
counts 9-digit numbers with exactly two digits each repeated twice (7 distinct digits, two appear twice, two absent).
Choose 2 digits for repetition: 
ways.
Choose 2 absent digits: 
ways.
Arrange: 
ways.
.
.
Therefore 
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