document.write( "Question 1045303: How many three-digit number are there with no dight reapeated?
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Algebra.Com's Answer #660705 by KMST(5328) $\"\"$ $\"About$

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ONE WAY TO LOOK AT IT:
\n" ); document.write( "Taking $\"3\"$ different digits, out of the $\"10\"$ available,
\n" ); document.write( "we can make $\"10%2A9%2A8=720\"$ different three-digit strings,
\n" ); document.write( "but the one starting with zero, such as $\"012\"$ or $\"097\"$ , cannot be considered three-digit numbers.
\n" ); document.write( "Among the $\"720\"$ three-digit strings, there are a few that start with zero.
\n" ); document.write( "How many? As many as the number of two-digit strings we can make using the $\"9\"$ non-zero digits,
\n" ); document.write( " $\"9%2A8=72\"$ .
\n" ); document.write( "That leaves us with $\"720-72=highlight%28648%29\"$
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\n" ); document.write( "ANOTHER WAY TO LOOK AT IT:
\n" ); document.write( "When trying to write a three-digit number are there with no digit repeated,
\n" ); document.write( "you have $\"9\"$ choices for the hundreds digit, because you would not start with $\"0\"$ .
\n" ); document.write( "After you choose your hundreds digit, there are $\"10-1=9\"$ other, different digits left to choose your tens digit from.
\n" ); document.write( "After you have chosen the first $\"2\"$ digits,
\n" ); document.write( "there are $\"10-2=8\"$ other, different digits left to choose your units digit from.
\n" ); document.write( "All in all, you have $\"9%2A9%2A8=highlight%28648%29\"$ different three-digit number are there with no digit repeated. \n" ); document.write( "

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