#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

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.