Use what you have learned about permutations to work out the following problems. The sum and/or product rule may also be required. i Six people, all of whom can play both bass and guitar, are auditioning for a band. There are two spots available: lead guitar, and bass player. In how many ways can the band be completed? Your friend Garth tries out for a play. After the auditions, they text you that they got one of the parts they wanted, and that (including them) nine people tried out for the five roles. You know that there were two parts that interested them. In how many ways might the cast be completed (who gets which role matters)? You are creating an 8-character password. You are allowed to use any of the 26 lower-case characters, and you must use exactly one digit (from 0 through 9) somewhere in the password. You are not allowed to use any character more than once. How many different passwords can you create? How many 3-letter \"words\" (strings of characters, they don't actually have to be words) can you form from the letters of the word STRONG? How many of those words contain an s? (You may not use a letter more than once.) How many permutations of {0, 1,2, 3,4, 5, 6} have no adjacent even digits? For example, a permutation like 5034216 is not allowed because 4 and 2 are adjacent. e o eI E] EREIR |