Suppose that the captain of a ship that is in distress must send a total of twelve different signals in succession. The twelve signals com-
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- A certain discrete mathematics class consists of 3131 students. Of these, 1414 plan to major in mathematics and 1818 plan to major in computer science. Five students are not planning to major in either subject. How many students are planning to major in both subjects? Number of students majoring in both =In a famous study done in the 1960s two dolphins, Doris and Buzz, were trained to work together to earn fish. Doris was shown a light underwater. If the light was on steadily, her partner Buzz on the other side of the tank needed to press a button on the right for them to earn fish. If the light was blinking, he needed to press a button on the left. At one point in the study, the researcher hung a canvas in the middle of the tank in such a way that Buzz could not see the light. After looking at the light, Doris "swam near the curtain and began to whistle loudly. Shortly after that Buzz whistled back and then pressed the correct button". (Tintle, Rossman and Chance, MAA Prep Workshop) Of course, getting it right once was not enough to convince the scientists that there was really communication going on. It turned out, that in 15 out of 16 trials the dolphin pushed the correct button. Of course, it is possible that this happened just out of random chance - that the second dolphin just…In a digital circuit, what will be the output of an OR gate that has 4 inputs, in which, one input is high and the other three are low? a. High or law depending on relative magnitudes of inputs b. Alternatively high and low c. Low d. High
- With a short time remaining in the day, a delivery driver has time to make deliveries at 6 locations among the 8 locations remaining. How many different routes are possible?A student works in a bookstore where he is required to work at least four and at most five days a week, at least one of which has to be a weekend day (Saturday or Sunday). How many different weekly work schedules can this student have?Certain app allows you to order from different types of cuisine. According with the app's records 23% of the orders are to an American food restaurant, 38% to an Asian food restaurant, 17% to a Mexican food restaurant, 6% to a Dessert place, and the rest are to other types of restaurants. Assume that incoming orders are independent of each other.
- Show that in a group of people there must be two individuals that have the same number of friends within the group.Suppose that the captain of a ship that is in distress must send a total of eleven different signals in succession. The eleven signals com- prise of 4 blue light signals (B1, B2, B3 and B4), 4 purple light signals (P1, P2, P3 and P4) and 3 red light signals (R1, R2 and R3). He must send the signals one after another at 1 minute intervals. In how many different ways may the captain send the signals if the purple light signals are the first 4 signals and the red light signals are the last 3 signals? [Answer]After a 30-member battalion fled, the general ordered the battalion to suffer decimation as punishment. In a decimation, one of out of every ten soldiers is killed. Assuming they are killed at the same time (so that it doesn't matter what order they are chosen), how many ways can the battalion be decimated?
- At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³One morning Dave an email message to Alvin that said the following: “You are one of my dearest friends. If you care about me, send a copy of this letter to two of your dearest friends tomorrow. If you do not break this chain, you will live long and prosper.” Alvin followed the directions: the next day he sent a copy of the message to two of his dearest friends. The following day, each of the recipients did the same. Count the day Dave sent the original message as the first day, and assume the chain is unbroken. A. How many copies of the message will be sent on the sixth day? B. Find the n-rule that will show how many copies of the message will sent on the n-th day.With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different locations among the 7 locations remaining. How many different routes are possible?