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20061ee131A_1_131A1HW

# 20061ee131A_1_131A1HW - randomly what is the probability...

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EE 131A Homework #1 Winter 2006 Due January 26 th K. Yao Read Leon-Garcia, Chap. 1; Chap. 2 (pp. 23–48) 1. A ”combination lock” has 5 numbers. The first three numbers are taken from the set { 0 , 1 , . . . , 9 } , the next number is taken from { 0 , 1 , 2 , 3 , 4 } , while the last number is taken from { 0 , 1 } . Find all the possible numbers for this lock. 2. From 2 digit numbers { 00 to 99 } , how many numbers will have exactly only 1 digit greater than 6 ? 3. A person has 5 different pairs of shoes and he never wears the same pair on two consecutive days. In how many ways can he wear these shoes in 4 days ? 4. How many distinct ”words” of eight letters may be formed from three A’s, two B’s, C, D, and E? 5. A child takes four volumes of an encyclopedia from a bookshelf. If they are put back
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Unformatted text preview: randomly, what is the probability that they are in the correct order? 6. In how many diﬀerent ways can we obtain exactly seven heads on 10 tosses of a coin? 7. A fast food counter contains onions, relish, mustard, catsup, and hot peppers for the hot dog. How many combinations are possible using one ingredient? Using two? What is the sum of all the possible combinations (including no ingredients)? 8. A lot of 20 items contains 3 defective items. 5 items are chosen at random and tested. What is the probability that 2 are found defective ? You can leave your answer in the form of ratio of factorials. 1...
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