# How many positive numbers can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 so that they are smaller than 800? The digits can repeat.

##### 1 Answer

#### Explanation:

These are numbers less than

So, make three slots:

## _ _ _

The first slot can be filled with only

Since repetition is allowed, the second and third slot can be filled in

Now, multiply the number of ways:

But wait, if we think about this, we notice that we can also form two-digit numbers and one-digit numbers less than

We can form

Now let's solve for the number of two-digit numbers. So put two slots:

## _ _

We can write

So there a total of

Now, add all the numbers:

Hope this helps!!! ☺•☻