Question

How many five-digit numbers can be formed by rearranging the digits in the number 93,218?

Answer 1

`5! = 120`

Explanation:

Let's imagine that we've got the five digits and have them scattered about, with the different places (ones, tens, hundreds, thousands, ten thousands) open and ready to accept a digit. What can we put into the ten-thousands place? There are 5 digits lying about - we can grab one of the 5 and stick it in.

And then we can grab one of the remaining 4 digits and place that in the thousands place.

And then we can grab one of the remaining 3 digits and place that in the hundreds place.

And then we can grab one of the remaining 2 digits and place that in the tens place.

And lastly we have the last digit going in the ones place.

That means we have:

`5xx4xx3xx2xx1=5! = 120`