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Five digit numbers are formed using the digits 0,1,2,3,4. Out of these numbers in how many numbers at least one number is repeated?

$\begin{array}{1 1} 96 \\ 120 \\ 2500 \\ 2404 \end{array}$

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If repetitions are allowed, the no. of 5 digit numbers =
$4\times 5\times 5\times 5\times 5=2500$
(since '0' cannot come in first place)
No. of 5 digit numbers in which no number is repeated=
$4\times 4\times 3\times 2\times 1=96$
$\Rightarrow\:No. of numbers in which at least one digit is repeated=
$2500-96=2404$
answered Aug 15, 2013 by rvidyagovindarajan_1
 

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