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The number of 5-digit telephone numbers having atleast one of their digits repeated is

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The number of 5-digit telephone numbers having atleast one of their digits repeated is

(A) 90,000 

(B) 10,000 

(C) 30,240 

(D) 69,760

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Answer is (D) 

Total number of telephone numbers when there is no restriction = 105 Also number of telephone numbers having all digits different = 10P5 Required number of ways = 105 – 10P5 = 1000000 -10x9x8x7x6 = 1000000 - 30240 = 69760

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