Question

Find all three-digit numbers with different digits, with each digit odd.

Answer 1

Find the total number of three-digit numbers with each digit odd and different

We know that there are $5$ odd numbers from $0$ to $9$. They are $1,3,5,7$ and $9.$

In a three-digit number, we have $5$ options to be put in the first digit place.

But since each digit in a number has to be different, the number of options we have in the second place will reduce to $(5-1)$, i.e., $4$.

Similarly, the number of options we have in the third-place will reduce to $(4-1)$, i.e., $3$.

So, total number of three-digit numbers with each digit odd and different $=5\times 4\times 3=60$
Hence, the total number of three-digit numbers with each digit odd and different is equal to $60$.