A combination lock requires five selections of characters. Each character is either an integer from 0 through 9, an upper-case letter from A through Z, or a lower-case letter from a through z. In other words, there are 62 characters to choose from (10 numbers, 26 upper-case letters, and 26 lower-case letters). Moreover, the locks are constructed in such a way that no character may be used more than once (a) How many different combinations are possible? (b) What is the probability that a randomly chosen combination will have no numbers?

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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.