1) If I am to paint our house by myself, it will take 4 days to complete painting the house. If my wife is to paint the house alone, it will take 6 days to complete her work. How many days will it take to paint our house if we decide to work together (without fight)? (a) 4 (b) 3.5 (c) 3 (d) 2.4 (e) 2 2) Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if one particular physicist must be on the committee? (a) 1 C (b) 12 C3 (c) sC2 . 7C2 (d) sC2 . 6C2 (e) 105 3) You have four identical Campbell cans of tomato soup. How many different ways can you hand out all the cans of soup to 5 people, if no person gets more than one can of soup? (a) 54 (b) 43 (c) 5 P4 (d) sC4 (e) 20 4) The U.S. Senate consists of 100 senators, two from each state. A committee consisting of 5 senators is to be formed. How many different committees are possible if no state will have both of its senators on the committee? (a) 100 Ps (b) 100 Cs (c) 100Cs . sC2 (d) 50Ca .2C1 (e) 50Cs . 32 5) License plates in a certain state consists of 5 digits and an ending letter of the alphabet. In how many different possible plates can be produced if all digits and letters are possible, with exception that the first digit cannot be 0 and the letter cannot be "O." ? (a) 105 - 26 (b) 5! . 10 - 25 (C) 10 Ps - 25P1 (d) 10Cs . 25C1 (e) 9- 104 . 25 6) In how many different ways can four distinct balls be put in six distinct containers so that the first container gets exactly one ball? (a) 4 P1 . 53 (b) 4C1 . 53 (c) 4CI . sC's (d) 4C1 . sP, (e) 24 7) A combination lock uses three numbers between 1 and 93 with repetition, and they must be selected in the correct sequence. Is the name "combination lock" appropriate? Why or why not? (a) Yes, because the combinations rule would be used to determine the total number of com- binations. (b) No, because the fundamental counting rule would be used to determine the total number of combinations. (c) No, because the permutations rule would be used to determine the total number of combi- nations. (d) No, because factorials would be used to determine the total number of combinations. (e) No, because the total number of combinations would be simply 93.[9](15) An advertising executive is studying television viewing habits of married men and women during prime-time hours. Based on past viewing records, the executive has determined that during prime-time, husbands are watching television 60% of the time. When the husband is watching television, 40%% of the time the wife is also watching. When the husband is not watching television, 30%% of the time the wife is watching television. al Construct a contingency table utilizing the above information. Wife Yes No Total Yes Husband No Total 1.00 Table 1: Watching TV? bj Are the event that the husband is watching and the event that the wife is watching during prime- time hours mutually exclusive? c) Are the event that the husband is watching and the event that the wife is watching during prime- time hours independent? d) What is the probability that both the husband and wife are watching during prime-time hours? el Find the probability that if the wife is watching television, the husband is also watching television
