Anagrams of LOLLIPOP

MediumCombinatorics~6m

How many distinguishable arrangements of the letters in LOLLIPOP\textbf{LOLLIPOP} begin and end with the same letter? (For example, LOLIPOPLLOLIPOPL counts - it starts and ends with LL.)

Show hints (2)+
  1. The boundary letter must repeat: only LL, OO, or PP qualify. Handle each case separately.
  2. For each, count distinct permutations of the remaining six middle letters (a multinomial), then add.

Answer

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300

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Asked at: Jane Street, Citadel

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