Question

How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 ? if 
(i) repetition of digit is allowed (ii) the repetition of digits is not allowed

Answer 1

So,

We are considering 3 digit numbers

When repetition is allowed

Let us solve this problem by taking cases, the three digit spaces be represented by _ _ _

So,

1 _ _ = 6×6 ways

2 _ _ = 6×6 ways

3 _ _ = 6×6 ways

4 _ _ = 6×6 ways

So,

Total number of ways = 4×6×6

=144 -1 (Because we took the case of 100 to which is equal to 100)

=143 ways

When repetition is not allowed,

Then

1 _ _ = 5×4 ways

2 _ _ = 5×4 ways

3 _ _= 5×4 ways

4 _ _ = 5×4 ways

Total number of ways = 80 ways

Answer 2

Step-by-step explanation:

Since repetition of digits is allowed :

No.of ways in filling the unit place = 6

No.of ways in filling the tens place = 6

No.of ways in filling the hundreds place =4 (except 0 & 5)

By the product rule,

Required no.of 3 digit numbers = 6×6×4

= 144