We want to build a chatbot, so we put together a list of 10 nouns, 10 verbs, and 10 objects, so we can construct sentences of the form NOUN VERB OBJECT (e.g., "Everyone loves combinatorics"). But we notice that 3 of the words on the noun list also appear on the verb list. None of the words on the object list appear on either of the other two lists. How many sentences of the form NOUN VERB OBJECT can we make if we require that the NOUN and VERB be different words?

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A: The objective of the question is to find out the number of ways to choose 6 objects from 15 distinct…

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A: Permutations and combinations

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A: An operation "∘" is associative if(x ∘ y) ∘ z = x ∘ (y ∘ z) for every three elements x, y and z in…

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A: The answer is given below:

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A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: In the first year, students from Business and Finance program have to take exactly 11 courses to…

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