Modify Example 9.2.4 by supposing that a PIN must not

Chapter 9, Problem 9.58

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Modify Example 9.2.4 by supposing that a PIN must not beginwithanyofthelettersAMandmustendwithadigit. Continue to assume that no symbol may be used more than once and that the total number of PINs is to be determined. a. Find the error in the following solution. Constructing a PIN is a four-step process. Step 1: Choose the left-most symbol. Step 2: Choose the second symbol from the left. Step 3: Choose the third symbol from the left. Step 4: Choose the right-most symbol. Because none of the thirteen letters from A through M may be chosen in step 1, there are 3613=23 ways to perform step 1. There are 35 ways to perform step 2 and 34 ways to perform step 3 because previously used symbols may not be used. Since the symbol chosen in step 4 must be a previously unused digit, there are 103=7 ways to perform step 4. Thus there are 2335347=191,590 different PINs that satisfy the given conditions. b. Reorder steps 14 in part (a) as follows: Step 1: Choose the right-most symbol. Step 2: Choose the left-most symbol. Step 3: Choose the second symbol from the left. Step 4: Choose the third symbol from the left. Use the multiplication rule to nd the number of PINs that satisfy the given conditions.