Question

Find the number of all five digit numbers which have atleast one repeated.

Answer 1

To find the number of 5 digit number , we need to multiply the possibilities for each digit. 9 possibilities for the first digit (1-9) and 10 possibilities for the remaining digits (0-9) $=9\times 10\times 10\times 10\times 10=90000$

Now, to find numbers that don't repeat any digits. The second digit cannot be equal to the first. The third cannot equal to first and second.The Fourth cannot equal to first , second and third. And the fifth cannot equal to first , second ,third and fourth.

So possibilities will be $=9\times 9\times 8\times 7\times 6=27216$

Number repeat at least one digit $=90000-27216=62784$