#902 · Combinatorics · Counting

Maximum permutations of binary letters

Show that among all strings of length $2 n$ formed from the letters $a$ and $b$ , the number of distinct permutations is greatest when the string contains exactly $n$ $a$ 's and $n$ $b$ 's.

~5 minProof · checked by AIpermutationsbinary stringsmaximisation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XI. Permutations and Combinations, Examples XI.b, No. 32

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