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1. Suppose you have totally forgotten the combination to your locker. There are three numbers in the combination, and you're sure each number is different. The numbers on the lock's dial range from 0 to 35. If you test one combination every 12 seconds, how long (in days to the nearest hundredth) will it take to test all possible combinations?

1. Suppose you have totally forgotten the combination to your locker. There are three numbers in the combination, and you're sure each number is different. The numbers on the lock's dial range from 0 to 35. If you test one combination every 12 seconds, how long (in days to the nearest hundredth) will it take to test all possible combinations?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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III. Problem Solving (Counting techniques) Directions: solve the following problems and show your complete solutions. Qualent to zore score 1. Suppose you have totally forgotten the combination to your locker. There are three numbers in the combination, and you're sure each number is different. The numbers on the lock's dial range from 0 to 35. If you test one combination every 12 seconds, how long (in days to the nearest hundredth) will it take to test all possible combinations? 2. How many 3-letter code words can be formed if at least one of the letters is to be chosen from the vowels a, e, i, o, and u. 3. How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each? 4. How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no digit is used more than once. 5. From a standard deck of cards, how many ways can you pick a face card, then a spade? Provided you put the first card back? 6. From a standard deck of cards, how many ways can you pick a king, a heart, and then a five? Provided you put the cards back into the deck. 7. How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?
Transcribed Image Text:III. Problem Solving (Counting techniques) Directions: solve the following problems and show your complete solutions. Qualent to zore score 1. Suppose you have totally forgotten the combination to your locker. There are three numbers in the combination, and you're sure each number is different. The numbers on the lock's dial range from 0 to 35. If you test one combination every 12 seconds, how long (in days to the nearest hundredth) will it take to test all possible combinations? 2. How many 3-letter code words can be formed if at least one of the letters is to be chosen from the vowels a, e, i, o, and u. 3. How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each? 4. How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no digit is used more than once. 5. From a standard deck of cards, how many ways can you pick a face card, then a spade? Provided you put the first card back? 6. From a standard deck of cards, how many ways can you pick a king, a heart, and then a five? Provided you put the cards back into the deck. 7. How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?
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