document.write( "Question 549708: Show that the number of permutations which can be formed from 2n letters which are either a's or b's is greatest when the number of a's is equal to the number of b's. \n" ); document.write( "
Algebra.Com's Answer #357988 by Theo(13342)\"\" \"About 
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assume the number of letters is equal to 4.
\n" ); document.write( "you can have:
\n" ); document.write( "0 a's and 4 b's
\n" ); document.write( "1 a and 3 b's
\n" ); document.write( "2 a's and 2 b's
\n" ); document.write( "3 a's and 1 b
\n" ); document.write( "4 a's and 0 b's
\n" ); document.write( "when you have 0 a's and 4 b's, the permutation formula is:
\n" ); document.write( "4! / (0!*4!) = 1 possible permutations.
\n" ); document.write( "that would be:
\n" ); document.write( "bbbb
\n" ); document.write( "when you have 1 a and 3 b's, the permutation formula is:
\n" ); document.write( "4! / (1!*3!) = 4 possible permutations.
\n" ); document.write( "that would be:
\n" ); document.write( "abbb
\n" ); document.write( "babb
\n" ); document.write( "bbab
\n" ); document.write( "bbba
\n" ); document.write( "when you have 2 a's and 2 b's, the permutation formula is:
\n" ); document.write( "4! / (2!*2!) = 6 possible permutations.
\n" ); document.write( "that would be:
\n" ); document.write( "aabb
\n" ); document.write( "abab
\n" ); document.write( "abba
\n" ); document.write( "bbaa
\n" ); document.write( "baba
\n" ); document.write( "baab
\n" ); document.write( "when you have 3 a's and 1 b, the permutation formula is:
\n" ); document.write( "4! / (3!*1!)
\n" ); document.write( "this is the same as 4! / (1!*3!) which we already did to get you a total of 4 possible permutations.
\n" ); document.write( "that would be:
\n" ); document.write( "aaab
\n" ); document.write( "aaba
\n" ); document.write( "abaa
\n" ); document.write( "baaa
\n" ); document.write( "when you have 4 a's and 0 b's, the permutation formula is:
\n" ); document.write( "4! / (4!*0!)
\n" ); document.write( "this is the same as 4! / (0!*4!) which we already did to get you a total of 1 possible permutation.
\n" ); document.write( "that would be:
\n" ); document.write( "aaaa
\n" ); document.write( "the formula peaks when the number of a's and b's is equal and goes symmetrically down from there on both sides of the peak.
\n" ); document.write( "this is characteristic of the formula.
\n" ); document.write( "it works with any number of a's and b's.
\n" ); document.write( " \n" ); document.write( "
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