The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.
Answer (integer)
243
Solution
<p>$C - 1:$ All digits are non-zero</p>
<p>${}^9{C_2}\,.\,2\,.\,{{3!} \over 2} = 216$</p>
<p>$C - 2$ : One digit is 0</p>
<p>$0,\,0,\,x \Rightarrow {}^9{C_1}\,.\,1 = 9$</p>
<p>$0,x,\,x \Rightarrow {}^9{C_1}\,.\,2 = 18$</p>
<p>Total $= 216 + 27 = 243$</p>
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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