1. A survey in 1986 asked households whether they had a VCR, a CD player or cable TV. 40 had a VCR. 60 had a CD player; and 50 had cable TV. 25 owned VCR and CD player. 30 owned a CD player and had cable TV. 35 owned a VCR and had cable TV. 10 households had all three. Find the total households for which the survey took place? (0.75 Mark) 2. Among 50 patients admitted to a hospital, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. Determine with the help of Venn Daigram: (a) The number of patients diagnosed with pneumonia or bronchitis (or both). (b) The number of patients not diagnosed with pneumonia or bronchitis. (1 Mark) 3. There are 5 green 7 red balls. Two balls are selected one by one without replacement. Find the probability that first is green and second is red. (0.75 Mark) 4. A library has 1,700,000 books, and the librarian wants to encode each using a code- word consisting of 3 letters followed by 3 numbers. Are there enough codewords to encode all 1,700,000 books with different codewords? (0.75 Mark) 5. A committee is to be chosen from among 8 scientists, 7 psychics, and 12 clerics. If the committee is to have two members of different backgrounds, how many such committees are there? (0.75 Mark) 6. Let A = {1,5,9, 11, 15, 23). (a) Find the number of sequences of length 3 using elements of A. (b) Repeat part (a) if no element of A is to be used twice. (c) Repeat part (a) if the first element of the sequence is 5. (d) Repeat part (a) if the first element of the sequence is 5 and no element of A is used twice. (1 Mark)