2018 AMC 10 B
Complete problem set with solutions and individual problem pages
How many subsets of contain at least one prime number? (2018 AMC 10B Problem, Question#5)
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Consider finding the number of subsets that do not contain any primes.There are four primes in the set：, , , and .This means that the number of subsets without any primes is the number of subsets of , which is just . The number of subsets with at least one prime is the number of subsets minus the number of subsets without any primes.The number of subsets is . Thus, the answer is .
Well, there are composite numbers, and you can list them in a number format, a number, number, and a number format. Now, we can use combinations. . Using the answer choices, the only multiple of is .
Subsets of indude a singe digit up to all eight numbers.Therefore,we must add the combinations of all possible subsets and subtract from each of the subsets fomed by the composite numbers.
Hence：
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