document.write( "Question 1194811: 16 books are to be lined up on the shelf. If 6 of the books are identical math books and 7 are identical Science books and 3 are identical English books, how many ways can they be lined up? \n" ); document.write( "
Algebra.Com's Answer #827086 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "If all 16 books were distinguishable from one another, then we'd have 16! = 20,922,789,888,000 possible permutations. The exclamation mark indicates a factorial.\r
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\n" ); document.write( "\n" ); document.write( "16! = 16*15*14*...*3*2*1 = 20,922,789,888,000
\n" ); document.write( "This massive number has 14 digits and the number is a bit under 21 trillion.\r
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\n" ); document.write( "\n" ); document.write( "That would be the answer if we could tell every book apart. However, 6 of the books are identical math books which we cannot tell apart. This means we have to divide by 6! = 6*5*4*3*2*1 = 720 to correct for the erroneous overcounting.
\n" ); document.write( "The same goes for the 7 identical science books and 3 identical English books.\r
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\n" ); document.write( "\n" ); document.write( "7! = 7*6*5*4*3*2*1 = 5040
\n" ); document.write( "3! = 3*2*1 = 6\r
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\n" ); document.write( "\n" ); document.write( "Overall we have to divide by 6!*7!*3! = 720*5040*6 = 21,772,800\r
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\n" ); document.write( "\n" ); document.write( "We get to
\n" ); document.write( "(20,922,789,888,000)/(21,772,800) = 960,960\r
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\n" ); document.write( "\n" ); document.write( "Answer: 960,960
\n" ); document.write( "It's not a typo that the \"960\" is written twice.
\n" ); document.write( "Delete the comma if necessary.
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