MIDM4U LESSON 4 ASSIGNMIENT \( \qquad \) 130 Name: \( \qquad \) PART A Multiple choice questions. Circle the best chotce [20 marks]. YOU MUST SHOW YOUR WORK! [1 mark for the correct answer and 1 mark show why you chose that answer in the space below the choices] 1. A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible types of pizza with one topping are there? a) 32 b) 128 c) 64 d) 256 e) None of these 2. A true or false test has 9 questions. How many answer keys are possible? a) 512 b) 128 e) None of these c) 164 d) 256 I 3. How many permutations are there of all the letters in the word BRIDE a) 32 b) 120 c) 64 d) 200 e) None of these 4. How many ways can John arrange 8 Cd 's on the shelf? a) 48000 b) 52060 c) 40320 d) 15560 e) None of these
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#3. For the following, you can leave your answer as a sum or product of binomial coefficients and or permutation notation (P(n,k)) where appropriate. (worth 7.5 points each for 30 points total). a) Suppose you're writing a Discrete Mathematics final and you have 22 questions in mind each covering a different topic. Due to time restrictions, you can only include 8 of these. How many different tests could you write? (assume order of the questions does not matter) b) Suppose you're taking a Discrete Mathematics final and there are 8 total questions. If you randomly pick a question to solve entirely before moving onto a new random question, how many different possible orders are there for you to solve the problems? Assume you have time to solve every problem. (For example, you may to do question 5 first, followed by question 2, then 7, 6, 1, 3, 8, and finally question 4). c) Suppose that 20 students take your discrete math final. The test is worth 150 points, so possible scores range from 0 to 150. After I've graded, how many ways are there for at least two students to have received the same score? (Hint: don't count this directly) d) Suppose that after all students take a Discrete Math final, they are given cookies. If I have 20 students and 40 cookies, how many ways are there to give at least one cookie to every student after they take the final exam?
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Direction: Choose the letter of the correct answer and write your answer on the space provided. Which of the following situations or activities order is important? A teenager girl selecting her outfit from blouses, skirts, and sandals. Choosing 3 out of your 5 friends to watch k-drama. Making your 10-character password for your Gmail account. Forming a dance troupe with 15 members. If P(n,4) = 120, what is n? d. 5 3. If we want to find the value of P(8,5) using the box method, how many factors will there be? d. 3 In how many ways can you arrange 10 different potted plants in a row? 10! b. 9! c. 8! d. 7! Which of the following is the same as 6 * 5 * 4 * 3? a. P(6,3) b. P(6,4) c. P(6,5) d. P(6,6) Find x if 52 + 2x! = 100. a. 24 b. 12 c. 4 d. 2
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16) 10! A) 3,628,800 B) 7,257,600 C) 362,880 D) 1,814,400 17) How many different 4-letter sequences can be made using the first 9 letters of the alphabet? Assume that repetition of letters is allowed. A) 24 B) 126 C) 6561 D) 3024 18) License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? A) 175,760 B) 100,000 C) 1,757,600 D) 11,881,376 19) A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections, how many ways can he arrange his program? A) 59,049 B) 45 C) 126 D) 15,120 20) How many ways can an IRS auditor select 5 of 13 tax returns for an audit? A) 120 B) 154,440 C) 371,293 D) 1287
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