Question 857969
<pre>
We can only use the digits 1,2,3,4, and 5

Number of 1-digit positive integers:

Pick the digit any 5 ways

That's 5 1-digit positive integers

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Number of 2-digit positive integers:

Pick the first digit any of 5 ways.
Pick the second digit any of 5 ways.

That's 5×5 or 5<sup>2</sup> 2-digit positive integers.

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Number of 3-digit positive integers:

Pick the first digit any of 5 ways.
Pick the second digit any of 5 ways.
Pick the third digit any of 5 ways

That's 5×5×5 or 5<sup>3</sup> 3-digit positive integers.

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Number of 4-digit positive integers:

Pick the first digit any of 5 ways.
Pick the second digit any of 5 ways.
Pick the third digit any of 5 ways.
Pick the fourth digit any of 5 ways

That's 5×5×5×5 or 5<sup>4</sup> 4-digit positive integers.

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Total = 5+5<sup>2</sup>+5<sup>3</sup>+5<sup>4</sup> = 5+25+125+625=780

Edwin</pre>