how many natural numbers less than 1000 can be formed with the digits 1,2,3,4and 5 if

1)no digits is repeated

2)repetition of digits is allowed

Dear Studentfriend Harmeet has given the correct answer for part 1.

Hi@Harmeet: Good effort! Keep posting!

Second part : When repetition of digits are allowed:

One digit number can be any of the five numbers 1, 2, 3, 4 or 5, so it can be done in five ways.

The no. of natural numbers with two digits: 

Unit place can be filled in any of the five ways.

Tens place can be filled in any of the five ways.

Thus, number of ways for two digit numbers = 5 × 5 = 25

Similarly, no. of natural numbers with three digits = 5³ = 125

Hence total number of natural numbers = 5 + 25 + 125 = 155