Question

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

Answer 1

Digits are $0,1,2,3,4,5$

Between $100$ and $500$

i) Repetition allowed

$0,5$ can not be at the hundredth place

$100$ is to be excluded

so the total number of numbers can be formed $=6\times 6\times 4-1=143$

ii) Repetition not allowed

Hundredth place $=4$

Tenth place $=5$

Once place $=4$

Total $=4\times 5\times 4=80$