How many license plates can be made out of 3 letters and 3 digits if the first and the last symbol must be a digit?

These are my thoughts:

At the first and last positions we must have a digit, so there are 10 possibilities in each of those slots.

For the remaining four slots we must have 3 letters and 1 digit, but the order does not matter.

So in 3 of these slots we have 26 possibilities, and in one of these slots we have 10 possibilities.

In addition, there are 4 different slots that we could put the digit in.

So, the number of ways to construct such a license plate would be: 10 * 26 * 26 * 26 * 10 * 4 * 10 = 70304000.

Is this true?