Numbers provided are 0, 1, 3, 4, 6, 7, 8 .How many odd numbers are less than 500 with conditions that these numbers couldn't be repeated? A.40, B.42, C.46, D.48, E.50

Question

Please someone help me. I can't understand this. Your help will be appreciated :)

Answer 1

Given the numbers can't be repeated and the number is odd number and the number is less than 500:

Let's start with one digit number:

We cannot form one digit number, because 0 would be repeated for the first two digit

Then, two digit number: (assume 0 is the first digit)

The last digit has to be 1, 3, or 7

The first digit can be 1, 3, 4, 6, 7, 8

Given the last digit is 1: then there will be 5 numbers

The same goes for the last digit is 3 and 7

So, total up, there are 15 numbers here

Lastly, three digit number:

Similarly, the last digit is 1, 3, or 7

The first digit can only be 1, 3, 4

The second digit can be 0, 1, 3, 4, 6, 7, 8

Given the last digit is 1: then the combination for the first 2 digits will be (2)(5) = 10

Same goes for last digit is 3

When the last digit is 7: the combination for the first 2 digits will be (3)(5)

Thus, there is 10 + 10 + 15 = 35 numbers here

In total, there will be 35 + 15 = 50 odd numbers