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QJEEM22Macf9d: JEE Main 2022 Mathematics - Class 11 JEEM22Macf9d Solution: The total number of three-digit numbers, with one digit…

The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.

Step-by-Step Verified Solution

C−1:C - 1: All digits are non-zero

9C2 . 2 . 3!2=216{}^9{C_2}\,.\,2\,.\,{{3!} \over 2} = 216

C−2C - 2 : One digit is 0

0, 0, x⇒9C1 . 1=90,\,0,\,x \Rightarrow {}^9{C_1}\,.\,1 = 9

0,x, x⇒9C1 . 2=180,x,\,x \Rightarrow {}^9{C_1}\,.\,2 = 18

Total =216+27=243= 216 + 27 = 243

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