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Discrete Math

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1.Using the principle of inclusion-exclusion find the numbers of integers between 1 and 1000 (inclusive)that are divisible by at least one of 2,3,5,or 7?

2.A drug store sells gum, candy, and playing cards. 15 teenagers are in the store...the clerk notes after the teenagers leave that 10 bought gum, 7 bought candy, and 12 purchased playing cards. 5 bought gum and candy,6 bought gum and playing cards and 2 purchased candy and playing cards...Why is the clerk so upset?

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