Part V: Counting (15 pt.) Answer each of the following questions. 1. (2.5 pt.) H
ID: 3322645 • Letter: P
Question
Part V: Counting (15 pt.) Answer each of the following questions. 1. (2.5 pt.) How many different permutations of the letters ABCDEFGH contain the strings CAB and BED? 2. (2.5 pt.) How many different bit strings of length 12 start with two 1's or have exactly five 0's (or both)? 3. (2.5 pt.) There are 25 students in a discrete math class. 10 are freshmen and 15 are sophomores. How many different ways are there to form a study group with 6 students from the class if at least one of them must be a freshman? 4. (2.5 pt.) A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) and 4 possible suits (spades, clubs, diamonds, hearts). There are 13 cards of each suit (one for each rank). A hand of 5 cards is called a straight flush if it contains 5 cards of the same suit that have consecutive ranks (for example, 3 -4 -5-6 -74). Note that an ace can be considered either the lowest rank or the highest rank. How many different hands of 5 cards are a straight flush? 5. (2.5 pt.) A bagel shop sells plain bagels, sesame bagels, onion bagels, and raisin bagels. How many different ways are there to choose a dozen bagels if at most 6 can be plain bagels? 6. (2.5 pt.) A package of baseball cards contains 20 cards. How many packages must be purchased to ensure that two cards in these packages are identical if there are a total of 550 different cards?Explanation / Answer
1)
the number of permutations = 4! = 24
because CAB and BED both contains B therefore CABED must be a string.