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📰 A linguist is analyzing the evolution of a certain languages vocabulary by categorizing words into 5 types: nouns, verbs, adjectives, adverbs, and function words. If she selects 8 words randomly from a pool where each type is equally represented, what is the probability that exactly 3 of them are nouns, 2 are verbs, 2 are adjectives, and 1 is an adverb?
📰 We need exactly 3 nouns, 2 verbs, 2 adjectives, and 1 adverb in a selection of 8 words. The number of ways to arrange these selections is given by the multinomial coefficient:
📰 Thus, the multinomial coefficient is:
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