The number 42 has the prime factorization 2- 3. 7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1· 42, 2- 21, 3· 14, and 6 - 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P2 P3P4, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f, and f. Then f, corresponds to a subset of {P1 P2: P3 Pa, and f, corresponds to the complement of that subset.) (c) If n = P, P2P3PaPs, where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n= Pi 2 P where the p, are distinct prime numbers, how many ways can n be written as product of two positive integer factors?

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.