b. Salt it. Another strategy is to start with a word or phrase that is easy to r

Question

b. Salt it. Another strategy is to start with a word or phrase that is easy to remember and then add some random changes to it. Bob starts with Superman and then applies one modification to it where a modification consists of inserting a number at some position. This process can produce a string like Super5man bl. How many different strings can Bob create starting with Superman? Suppose Bob wants to apply two modifications to produce a string like 9Supersman or a string like Super95man. We want to determine the dif ferent strings Bob can create. He does this in two steps: Step 1 Choose the first number say 5) and insert it in Superman. (It produces Super5man, etc.) Step 2. Choose the second number (say 9) and insert it in the string obtained after Step 1. (If the string from step 1 was Super5man, then the result can be 9Super5man or Super95man, etc.) b2. To determine the number of different strings Bob can create, we can just apply the Product Rule (Handout 8, page 3). Explain why the product

Explanation / Answer

b1. There are 10 numbers and 9 different positions. So, number of possible strings = 10*9 = 90

b2. Strings where digits are inserted consecutively will be counted twice. For example, the string super95man or sup95erman can be created either by inserting 9 first or 5 first. This will get overcounted.

b3. Number of possible strings in step 1 = 90.

in step 2, number of positions = 10. So number of possibilities = 90*100 = 9000.

Number of duplicates = 9*(10*10) = 900

So, number of possible combinations = 9000-900 = 8100

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