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Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

Telephone Numbers In the past, a local telephone number in the United States consisted of a sequence of two letters followed by five digits. Three letters were associated with each number from 2 to 9 (just as in the standard telephone layout shown in the figure) so that each telephone number corresponded to a sequence of seven digits. How many different sequences of seven digits were possible?

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To determine

To calculate: The number of different sequences of 7 digits where telephone numbers consist of sequences of 2 letters followed by 5 digits and 3 letters are associated with each number from 2 to 9 and each telephone number correspond to a sequence of 7 digits.

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Explanation

Given Information:

The telephone numbers consist of sequences of 2 letters followed by 5 digits and 3 letters are associated with each number from 2 to 9 and each telephone number correspond to a sequence of 7 digits and the provided figure is

.

Formula used:

The Decision Algorithm is to make a set of decisions to determine the number of possible outcomes.

The Addition Principle is, if there is a choice among r disjoint alternatives and alternative 1 has n1 possible outcomes, alternative 2 has n2 possible outcomes and so on and alternative r has nr possible outcomes with no two outcomes same, then the total number of outcomes are n1+n2++nr.

The Multiplication Principle, if there is a sequence of choice with r disjoint steps and step 1 has n1 possible outcomes, step 2 has n2 possible outcomes and so on and step r has nr possible outcomes with no two outcomes same, then the total number of outcomes are n1×n2××nr.

Calculation:

Consider the telephone numbers consist of sequences of 2 letters followed by 5 digits and 3 letters are associated with each number from 2 to 9 and each telephone number correspond to a sequence of 7 digits and the figure

Use the Decision Algorithm to make a set of decisions to determine the number of possible outcomes

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