(C) Let the three-digit number be represented as $abc$, where $a, b, c$ are the digits.According to the problem, $b = c$ and $a \neq b$.The first digi

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(C) Let the three-digit number be represented as $abc$, where $a, b, c$ are the digits.According to the problem, $b = c$ and $a \neq b$.The first digit $a$ can be any digit from $1$ to $9$ ($9$ choices).The last two digits $b$ and $c$ must be equal, so we choose a digit $x \in \{0, 1, 2, \dots, 9\}$ for both $b$ and $c$.Since $a \neq b$, for each choice of $a$, there are $10 - 1 = 9$ possible choices for the pair $(b, c)$.Total number of such $n$'s $= 9 \times 9 = 81$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

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AP EAMCET 2005 All AP EAMCET

A
$64$
B
$72$
C
$81$
D
$900$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

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