document.write( "Question 1160018: If three people roll a dice once, how many ways can the sum of the three people’s rolls add up to exactly 9? \n" ); document.write( "

Algebra.Com's Answer #783197 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The \"stars and bars\" method used by another tutor is a good tool for problems like this where the numbers are larger, and where there are no restrictions on how large the numbers can be.

\n" ); document.write( "However, direct use of the stars and bars method for this problem gives a wrong result, because the integers are restricted to the range 1 to 6 inclusive. So counting the number of ways by enumeration is necessary.

\n" ); document.write( "I would assume, unlike one of the other tutors, that, for example, 1+3+5 is a different result than 3+1+5....


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document.write( "  combinations    number of
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document.write( "   with a sum   permutations
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document.write( "     of 9
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document.write( "  --------------------------
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document.write( "    1+2+6         3! = 6
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document.write( "    1+3+5         3! = 6
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document.write( "    1+4+4      3!/2! = 3
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document.write( "    2+2+5      3!/2! = 3
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document.write( "    2+3+4         3! = 6
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document.write( "    3+3+3      3!/3! = 1
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document.write( "  ------------------------
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document.write( "            total:    25

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document.write( "ANSWER:  There are 25 ways for the sum of the numbers on the three people's dice to be 9.

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