A survey of households in the United States reveals that 96% have at least one television set, 98% have telephone service, and 95% have telephone service and at least one television set. What percentage of households in the United States have neither telephone service nor a television set?

Find the value of each of these quantities. a) P (6, 3) b) P (6, 5) c) P (8, 1) d) P (8, 5) e) P (8, 8) f) P (10, 9)

How many elements are in the union of four sets if the sets have 50, 60, 70, and 80 elements, respectively, each pair of the sets has 5 elements in common, each triple of the sets has 1 common element, and no element is in all four sets?

Find the number of elements in

$$A_1 ∪ A_2 ∪ A_3$$

if there are 100 elements in each set and if a) the sets are pairwise disjoint. b) there are 50 common elements in each pair of sets and no elements in all three sets. c) there are 50 common elements in each pair of sets and 25 elements in all three sets. d) the sets are equal.

What is the probability that the sum of the numbers on two dice is even when they are rolled?

In a survey of 270 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower, 26 like both brussels sprouts and broccoli, 28 like both brussels sprouts and cauliflower, 22 like both broccoli and cauliflower, and 14 like all three vegetables. How many of the 270 students do not like any of these vegetables?

How many ways are there to arrange the letters a, b, c, and d such that a is not followed immediately by b?

How many permutations of the letters ABCDEFG contain a) the string BCD? b) the string CFGA? c) the strings BA and GF? d) the strings ABC and DE? e) the strings ABC and CDE? f) the strings CBA and BED?

What is the probability that a five-card poker hand does not contain the queen of hearts?

How many bit strings of length 10 contain a) exactly four 1s? b) at most four 1s? c) at least four 1s? d) an equal number of 0s and 1s?

How many bit strings of length seven either begin with two 0s or end with three 1s?

Suppose that Frida selects a ball by first picking one of two boxes at random and then selecting a ball from this box at random. The first box contains two white balls and three blue balls, and the second box contains four white balls and one blue ball. What is the probability that Frida picked a ball from the first box if she has selected a blue ball?

Find the number of elements in A₁ ∪ A₂ ∪ A₃ if there are 100 elements in A₁, 1000 in A₂, and 10,000 in A₃ if a) A₁ ⊆ A₂ and A₂ ⊆ A₃. b) the sets are pairwise disjoint. c) there are two elements common to each pair of sets and one element in all three sets.

How many students are enrolled in a course either in calculus, discrete mathematics, data structures, or programming languages at a school if there are 507, 292, 312, and 344 students in these courses, respectively; 14 in both calculus and data structures; 213 in both calculus and programming languages; 211 in both discrete mathematics and data structures; 43 in both discrete mathematics and programming languages; and no student may take calculus and discrete mathematics, or data structures and programming languages, concurrently?