Published by:
CGP EDU Academic Team
Published on: August 12, 2026
How many 5 digit numbers can be made having exactly two identical digit.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
45360
Sol. case- I Two identical digit are (0, 0)
number of ways 9 C 3 
= 3024
case- II Two identical digit are
(1, 1), (2, 2) ...... (9, 9)
P-1 If '0' is included
9 C 1 . 8 C 2 = 
12096
P-2 If 0 is not included
9 C 1 . 8 C 3 
= 3360 × 9 = 30240
Total number of ways
9 C 1 8 C 2 + 
8 C 3 . 
= 12096 + 30240 = 42336
Total ways = 42336 + 3024 = 45360.
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