MATH1007⋅SESSION 2, 2021SGTA⋅WEEK 13⋅SOLUTIONS1. How manypalindromesare there with 5 characters? Stick to lower case letters, so an example wouldbe𝑟𝑟𝑎𝑟𝑟.
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2. We seek to put 6 bits of different junk mail into 8 letter boxes. How many ways can this be done? (Thisis a surprisingly difficult, and easy, question.)
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Consider holding all 6 bits of junk mail. How many choices to you have as to where to put the firstbit of mail? Any of the 8 mail boxes, so8choices. How many choices for the second bit of mail?
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3. Use an Excel spreadsheet (or something else) to calculate the probability of at least2peope sharing abirthday in a group of 24 people. (The answer is53.8%– assuming365days in the year.) Repeat for30people,50people and70people.
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4. How many strings are there of length 6, using the letters from𝑎to𝑧for each of the following specifica-tions.(a) There are no restrictions.
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