Answer:
With repetition: 125
Without repetition 60
Explanation:
The answer will depend on whether a digit can be repeated or not. For example, 333 uses only one of the 5 digits
We will consider both cases
(1) With repetition (numbers like 333, 335, 478 allowes)
For the units place we can pick a digit in 5 different ways: 3 4 5 7 8
For the tens place, since we can pick the same digit as before, there are 5 possible ways
For the hundreds place again 5 possible ways
So total number of ways to generate a 3 digit number from 3 4 5 7 8x 5 x 5 = 125.
(ii) Without repetition
There are 5 different ways to pick a digit for the units place from 3 4 5 7 8
Once we pick a digit for the units place, we cannot use that digit anymore so for the tens place we only have 4 ways to pick a digit
For the hundreds place you have only 3 ways to pick the digit since we have already picked 2 digits
Number of ways = 5 x 4 x 3 = 60