Question

What is the number of 6 digit telephone numbers which have at least one of their digits repeated?

Answer 1

Number will be formed by using 10 digits from 0 to 9.
At least one digit repeated = Total - (number when no digit is repeated)
Total = Each of the six places can be filled in 10 ways.
Hence total is ${10}^6$.
When no repetition is allowed then it will be ${}^{10}{P}_6$
In telephone numbers this is permissible
Required answer is ${10}^6{-}^{10}{P}_6$