三、Please calculate the number of positive integers greater than 1 (> 1) and not exceeding 150 (≤ 150) that are divisible by none of 3, 5, or 7 by using The Principle of Inclusion–Exclusion. You should explain your answer. (10%)

四、Paul has two coolers. Cooler 1 contains 8 cans of cola and 3 cans of lemonade. Cooler 2 contains 5 cans of cola and 7 cans of lemonade. Paul randomly selects one can from Cooler 1 and transfers it into Cooler 2. Subsequently, Betty randomly selects two cans from Cooler 2. Given that both of Betty's selections are cans of cola, what is the probability that the can Paul initially transferred was lemonade? (10%)

三、Please calculate the number of positive integers greater than 1 (> 1) and not exceeding 150 (≤ 150) that are divisible by none of 3, 5, or 7 by using The Principle of Inclusion–Exclusion. You should explain your answer. (10%)

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