Question

Total number of all telephone numbers of 4 digits in which at least one digit is repeated

Answer 1

Answer:

Let the repeated no. be given by 10C1.

So other two digits are given by 10C1 and 10C1.

Now arranging them, Cases :

• 2 same and 2 different : 10C1×10C1×10C1×4!/2!
• 3 same and 1 different : 10C1×10C1×10C1×4!/3!
• 2 same and 2 same of other type : 10C1×10C1×10C1×4!/(2!×2!)
• 4 same : 10C1×10C1×10C1×4!/4!

So Total ways(on adding all cases):

1000(12+4+6+1) = 23000 Numbers are possible.

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