[Math] How many 4-digit odd numbers can be formed using the digits 0, 1, 2 and 3 only if the repetition of the digit is not allowed

algebra-precalculuscombinationspermutations

As stated in the title above: How many 4-digit odd numbers can be formed using the digits 0, 1, 2 and 3 only if the repetition of the digit is not allowed?

I already have the answer for this and it is 8.

(2)(2)(1)(2) = 8

However, I do not understand how it became like that. Any understandable explanation would be appreciated!

Best Answer

Hint #1: Since the number is odd, then the unit's digit could only be either $1$ or $3$.

Hint #2: Since the number has $4$ digits, the thousand's digit cannot be $0$.

Can you finish?