document.write( "Question 1195254: Numbers are to be built using only the digits 1,2,3,4, and 5 in such a way that each digit is only used once in each number. How many of these numbers will have the following property?
\n" ); document.write( " (a) The first digit is divisible by one
\n" ); document.write( " (b) The first 2 digits make a number that is divisible by 2
\n" ); document.write( " (c) The first 3 digits make a number that is divisible by 3
\n" ); document.write( " (d) The first 4 digits make a number that is divisible by 4
\n" ); document.write( " (e) All 5 digits make a number that is divisible by 5 \n" ); document.write( "

Algebra.Com's Answer #827677 by lotusjayden(18) $\"\"$ $\"About$

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Numbers are to be built using only the digits 1,2,3,4, and 5 in such a way that each digit is only used once in each number. How many of these numbers will have the following property?
\n" ); document.write( " (a) The first digit is divisible by one
\n" ); document.write( " (b) The first 2 digits make a number that is divisible by 2
\n" ); document.write( " (c) The first 3 digits make a number that is divisible by 3
\n" ); document.write( " (d) The first 4 digits make a number that is divisible by 4
\n" ); document.write( " (e) All 5 digits make a number that is divisible by 5
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document.write( "(a) Since every number is divisible by one, then the total possible permutations are 5, as you can't repeat the numbers and order matters.\r
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document.write( "(b) Since every number that is divisible by two is even, then it must end in 2 or 4 in this situation. Therefore(you could easily count them), the total possible permutations are 8.\r
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document.write( "(c) Since every number divisible by 3 is determined by adding the digits together(if the digits add up to a multiple of 3, then it is divisible), the only possible solutions are when the digits are (1,2,3),(1,3,5), and (3,4,5), Where there are 6 possible permutations of each, so the total number of permutations are 18(6+6+6=18).\r
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document.write( "(d) Since every number that is divisible by two is determined by looking at the last two digits of a number. I know that the multiples of 4 up to 100, but we could only use the multiples of 4 up to 52. The multiples you could possibly choose are 12,24,32, and 52. Every one of them has 50, so there are50+50+50+50=200 total possible permutations.\r
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document.write( "(e) Since all multiples of 5 ends in 5 or 0, we exclude zero right away. After some counting, you end up with 24 possible permutations. \n" );
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