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Question

# 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 repeat?

A
9456745
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B
7898760
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C
8455680
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D
none of these
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Solution

## The correct option is C 8455680Total 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 106×9−(9.9.8.7.6.5.4)=9000000−544320=8455680

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