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

657 "numbers".

Explanation:

These are numbers less than 800, so they are at most 3 digit numbers.

So, make three slots:

_ _ _

The first slot can be filled with only 1,2,3,4,5,6 or 7 (7 "digits") because the number is less than 800. So, it can be filled in 7 ways.

Since repetition is allowed, the second and third slot can be filled in 9 ways each.
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Now, multiply the number of ways:

rarr7xx9xx9

color(green)(rArr567

But wait, if we think about this, we notice that we can also form two-digit numbers and one-digit numbers less than 800.

We can form 9 one digit numbers.

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

_ _

We can write 9 digits in each of the slots:

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So there a total of 9xx9=81 ways.

Now, add all the numbers:

rarr567+9+81

color(green)(rArr657

Hope this helps!!! ☺•☻