Question

The number of five-digit number that can be formed with the digits $0,1,2,3$ and $4$ if the digits can be repeated in the same number is

• A. $25$
• B. $250$
• C. $2500$
• D. $12500$

Answer 1

The correct option is C $2500$

Digits are $0,1,2,3,4$, total number of Digits $=5$

We know that as 0 cannot be placed in the thousandth place, thus the number of ways to fill up the ten thousandth place from the remaining 4 digits$=4$

We also know that as the numbers can be repeated thus the number of ways to fill up each of the other 4 places (thousandth, hundredth, tenth and ones places) $=5$

So the total number of ways to form a 5-digit number $=4\times 5\times 5\times 5\times 5=2500$