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# The numbers of five-digit telephone numbers having atleast one of their digits repeated

$\begin{array}{1 1}(A)\;90000\\(B)\;100000\\(C)\;30240\\(D)\;69760\end{array}$

Toolbox:
• $n!=n(n-1)(n-2)(n-3)......(3)(2)(1)$
No of numbers with repetition =$10\times 10\times 10\times 10\times 10$
$\Rightarrow 100000$
No.of numbers without repetition =$10\times 9\times 8\times 7\times 6$
$\Rightarrow 30240$
$\therefore$ No.of numbers with atleast one digit repeated =$10,0000-30240$
$\Rightarrow 69760$
Hence (D) is the correct answer.