Permutations/Combinations Assignment

T	C	A
10	5	15

• In an experiment on growing tomatoes, a researcher gathers 5 different cherry tomato plants, 4 different plum tomato plants, and 3 different roma tomato plants. She wishes to select 4 plants at random. How many ways can this be done if exactly 2 cherry tomato plants must be included? [3A]

• How many 7-digit even numbers can be formed using all the digits 0, 1, 2, 2, 3, 5, and 5? [3A]

• In the diagram, determine how many paths there are from point A to point B without going backwards. [3T]

• Special Euchre desk is a card game that uses only the Aces, Kings, Queens, Jacks, 10s, 9s, 8s, 7s of each suit. Seven-card hands are dealt to the players. What is the probability of selecting five face cards? [3A]

• An athletic committee with three members is to be randomly selected from a group of six gymnasts, four weightlifters, and eight long-distance runners. Determine the probability that:

• the committee is comprised entirely of runners [3A]

• the committee is represented by each of the three types of athletes [3T]

• To win the first prize you need to match seven numbers from 1 to 27 in no particular order. To win the second prize you need to match six of the seven winning numbers.
• What is the probability of winning the first prize? [3A]

• What is the probability of winning the second prize? [3T]

• You and your lab partner have made a list of six tasks you must do to complete your science project. In how many ways can you divide this work? Explain your reasoning. [2C]

• A university has a telephone system in which extension numbers are three digits long with no repeated digits and no 0's. The university has 492 telephones at present and is planning to add another 35 in the near future. Should the university change its system? Explain why with words. [2C]

• You are thinking of using some leftover ceramic tiles to make a decorative border for a patio. You have ten blue, four gold, and six white tiles. In how many ways can make the border if you use a total of six gold and white tiles and you want to use more gold than white? Explain your reasoning with math and words. [1C, 1T]