Question

discrete math do all please

2. Six people attend the theater together and sit in a row with exactly six seats. (a) In how many ways can they be seated together in the row? (b) Suppose one of the six is a doctor who must sit in a specific aisle seat in case she is paged. How many ways can the people be seated together in the row with the doctor in the aisle seat? (c) Suppose the six people consist of three married couples and each couple wants to sit next to each other. In how many ways is this possible if the husband must sit to the left of their wife? (d) Suppose the six people consist of three married couples and each couple wants to sit next to each other. In how many ways is this possible if all the couples care about is sitting next to each other (in either order)? (e) If the six people consist of three married couples, but all six are randomly assigned the seats in the row, what is the probability that everyone gets to sit next to their spouse? 3. A study was done to determine the efficacy of three different drugs - A, B and C-in relieving headache pain. Over the period covered by the study, 80 subjects were given the chance to use all three drugs. The following results were obtained: • 46 reported relief from drug A. • 39 reported relief from drug B. . 34 reported relief from drug C. • 25 reported relief from both drugs A and B. • 16 reported relief from both drugs B and C. • 22 reported relief from both drugs A and C. • 63 reported relief from at least one of drugs A, B or C. Note that no pair of these response categories are mutually exclusive. For example, some of the 46 subjects who reported relief from drug A may also have reported relief from drugs B or C. (Hint: Drawing a Venn-diagram might be helpful for this problem.) (a) How many subjects got relief from none of the drugs? (b) How many subjects got relief from all of the drugs? (c) How many subjects got relief only from drug A? (d) How many subjects did not get relief fro, drug C? 4. Consider making a 4-letter password out of the letters from the word WHALES (with possible repeti- tion). If the letters in the password are chosen at random, what is the probability that the letter W appears at least once?

Answer 1

2. There are & people sitting in a row with exactly 6 sents. (a) There are places to sit and 6 people are there, so total number of way is 6! - 685 AX 3X2X1 - 720. (6) If one of them is doctor who must sit in a specific daisle seat. There are two aisle seat. For each of these seats, the other can seat in 5! wags. So, total no. of warg is 275! = 2x120=240. (C) For this problem, another condition is there comple wants to send sit together must sit to the left side of their wife. So, we com a think couple as a single person and there are 3 seats. So, the number of wory is = 3! = 3x2=6. d) In this problem, couples are sitting together in any order. So, the number of wag is getting double from the previous problem. Because here Umbands are also com set. in the opposite side. So, no, of wargs = 2×3! = 12 le) from 1d), we see that total no, of ways that everyone gets to sit next to their spouse is 12, And total no. of way of sitting is 720,

So, if all sine are som domly assigned. Then the required probability will be - 12 = to 720 60