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Also give me the multinomial probability if the letter probabilities are 0.1, 0.4, 0.4, 0.1.","exampleUseCases":[{"title":"Scrabble word arrangement counting","prompt":"How many distinct arrangements of the letters in the word BALLOON are there? I need the multinomial coefficient and the formula."},{"title":"Probability of exact outcome mix","prompt":"If I have counts 2, 3, 1 and the outcome probabilities are 0.5, 0.3, 0.2, what is the multinomial probability of getting exactly those counts?"},{"title":"Combinatorics homework problem","prompt":"I need to find the number of distinct permutations of the sequence with group sizes 3, 2, 2, 1 — can you compute the multinomial coefficient and show me the formula?"}],"resultDescription":"Returns the multinomial coefficient (as a string, possibly in scientific notation), total number of items, the group sizes used, the formula string, a human-readable summary, and optionally the multinomial probability if outcome probabilities were supplied. 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