CIS 1166/Exam 3/ 6. You pick a bit string from the set of all bit strings of length ten. (a) What is the probability that the bit string has exactly two 1s? [R7.21] (b) What is the probability that the bit string has exactly two 1s, given that the string begins with a 1? [R7.22] 7. Suppose that a word is any string of seven letters of the upper case English alphabet, (do not evaluate expressions like 265 or 30!) a) How many words are there if repeated letters are allowed? [R6.1.1] b) How many words are there if repeated letters are not allowed? [R6.1.1] c) How many words begin with A or end with B (repeated letters allowed)[R6.1.5] 8. Consider all bit strings of length 12. a) How many begin with 110? [R6.1.14] b) How many have exactly 4 1s? [R6.1.17] 9. Show that in any set of 6 classes meeting once a week on a particular day of the week there must be at least 2 classes that meet on the same day assuming no weekend classes. [R6.2.1] 10. Suppose you have 30 books, 15 math books, 10 history books and 5 novels. Assuming all books are different, in how many ways can you: a) put the 30 books on a sufficiently long shelf? [R6.3.45] b) select a set of three history books and seven math books to give to a friend? [R6.3.47]