document.write( "Question 995681: How many 4-digit numbers greater than 1000 are there that use the four digits of 2012? \n" ); document.write( "

Algebra.Com's Answer #614465 by KMST(5328) $\"\"$ $\"About$

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If we put some distinguishing marks on the 2's,
\n" ); document.write( "we have 4 distinct items: $\"0\"$ , $\"1\"$ , $\"red%282%29\"$ , and $\"green%282%29\"$ .
\n" ); document.write( "The first digit cannot be $\"0\"$ , because that would make the number less than 100.
\n" ); document.write( "(It would really be a 3-digit number in disguise, too).
\n" ); document.write( "So, we have 3 choices for the first digit.
\n" ); document.write( "For each of those choices, there will be 3 items left, to chose a 2nd digit from, for a total of $\"3%2A3=9\"$ choices for the first two digits.
\n" ); document.write( "For each of those $\"9\"$ choices, we still have to choose one of the $\"2\"$ remaining elements as the third digit, giving us $\"2%5D%5D%5D+choices.%0D%0AThat+makes+%7B%7B%7B3%2A3%2A2=18\"$ sequences of 4 elements, where we can distinguish $\"red%282%29\"$ from $\"green%282%29\"$ .
\n" ); document.write( "However, taking those permutations of elements as numbers,
\n" ); document.write( "we would not distinguish between pairs with $\"red%282%29\"$ from $\"green%282%29\"$ in different orders,
\n" ); document.write( "like $\"10red%282%29green%282%29\"$ and $\"10red%282%29green%282%29red%282%29\"$ ,
\n" ); document.write( "which both represent number $\"1022\"$ .
\n" ); document.write( "So we need to divide by $\"2\"$ , to find that there are
\n" ); document.write( " $\"3%2A3%2A2%2F2=highlight%289%29\"$ numbers greater than 1000 that can be made using the four digits of 2012. \n" ); document.write( "

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