A Swedish watch company is assigning ID cards for its employees. The ID is made of 7 digits. How many ID numbers can exist such that at least one of the digits repeats?

9456745

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7898760

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8455680

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none of these

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Solution

The correct option is C 8455680
Option (c )

Total number of combinations = No repeats + 1 number repeat + 2 number repeat+.....7 number repeat

Total number of combinations - No repeats = 1 number repeat + 2 number repeat +...... 7 number repeat

Total number of combinations -No repeats = Atleast one number repeat

$10^{6} \times 9 - (9.9.8.7.6.5.4) = 9000000 - 544320 = 8455680$

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