document.write( "Question 1191507: Please help me solve this problem four children, identical twins, and identical triplets pose for a photograph. How many photographs can be made? \n" ); document.write( "
Algebra.Com's Answer #823298 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "I'm assuming the identical twins are separate from the four children mentioned at first. The same goes for the identical triplets.\r
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\n" ); document.write( "\n" ); document.write( "There are 4+2+3 = 9 kids in all
\n" ); document.write( "There would be 9! = 9*8*7*6*5*4*3*2*1 = 362,880 different permutations or orderings if we can tell the twins and triplets apart. \r
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\n" ); document.write( "\n" ); document.write( "However, we can't tell the twins apart, so we have to divide by 2 to fix the overcounting concerning the identical twins.
\n" ); document.write( "We also have to divide by 3! = 3*2*1 = 6 to account for the triplets we can't tell apart either.
\n" ); document.write( "Consider the set {A,B,C}. There are 6 ways to arrange those three items.\r
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\n" ); document.write( "\n" ); document.write( "Overall, the massive number calculated earlier is too large by a factor of 2*6 = 12
\n" ); document.write( "Meaning we have to divide that large figure by 12 to fix the error.\r
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\n" ); document.write( "\n" ); document.write( "(362,880)/12 = 30,240
\n" ); document.write( "Interesting side note: This is equivalent to 2*(9 P 5) though I'm not sure if it's a coincidence or not.\r
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\n" ); document.write( "\n" ); document.write( "Answer: 30,240
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