Alphabet Designs
Apr/110
Suppose the plates are designed so that the first three characters are letters of the alphabet?
HOPE you can help me 'coz I DO NOT KNOW how to answer these AND PLEASE DO NOT SHOW YOUR SOLUTIONS, THANK YOU 1. Suppose that license plates are designed so that the first three characters are letters of the alphabet and the other three characters are numbers. How many license plates can be produced in accordance with this conception? 2. A multiple choice test consists of 8 questions, each with 4 possible answers, but which one is correct how many ways a student can answer questions 8 and a. Get them all correct b. Ask them all wrong c. Get at least a good Reply 3. How many permutations are there of the word a. B. COMMITTEE C. Statistics MATHEMATICS d. PHILIPPINES e. MISSISSIPPI f. Barbiturates 4. An instructor of physics has its class a gambling problem consists of 10 problems and need each student to solve all the problems 8. How many ways can Arthur, a member of the class choose 8 of the problem?
1. The general counting principle states that if a probability experiment is determined by various tests, then the number of ways the experiment can result can be obtained by multiplying the number of ways each may be determined. There are 26 ways for each letter and 10 for each number (including zero), so there are 26 * 26 * 26 * 10 * 10 * 10 = 17,576,000 different plates possible. 2. a. There is only one way students can get the right of every problem, there is therefore 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 = 1 means to get all correct. b. Similarly, there are 3 ways he can get every problem wrong, so there are 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 6561 ways he can get it all wrong. c. Because each problem can be answered in 4 ways, the test can be answered in 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 65,536 ways. Of these, 6561 are all wrong, so 65536-6561 = 58,975 ways to get at least one correct. 3. I will do One is ridiculous to do all of them. a. If all the letters in the committee were different, then there would be 9! = 362,880 different permutations. However, Some letters are the same, so there is less than that, so we must divide by the number of ways to rearrange the letters, etc.. There is 1 C, 1 O, 2 M, 1 I, 2 T and 2 E, so there are 9! / (1! 1! 2! 1! 2! 2!) = 45,360 different permutations. bf parts are made in a similar manner. 4. As it has not matter what order the problems are taken, then you must find the number of combinations of 8, which can be selected from 10. 10C8 = 10! / (8! 2!) = 45 ways of selecting 8 of 10 problems.
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