Help me answer 9 to 17

1i].There are 909 3-digit integers, the integers between 109 and 999, inclusive. What percent of these integers contain mus? For example, 339. 5'11, 111 would be examples of such integers. 11. Given a set with 7" elements. Explain why there are the same number of subsets with 2 elements as there are subsets with 5 elements. 12. An n-bit string is a string of length n, that is, it is string of n symbols each of which is a 9 or a 1. The weight of a hit string is the number of 1's that it contains. How many 3-bit strings have weight equal to 4? 13. Solve the equation for n; G) = 45. Show algebraic solution. n!{n1]l [n_z)!{+2]! Show work. 14. Simplify the expression 15. A coin is tossed 3 times. What is the probability of obtaining exactly 2 tails? (Hint: make the sam pie space for tossing a coin three times) 15. A truevfalse quiz consists of 5 questions. What is the probability that the answers are all true or all false? (Hint: make a sample space.) 1?. Fifty tickets are marked with the rst 59 positive integers. If one ticket is drawn at random, what is the probability that it is either a multiple of 5 or a multiple of 3? Directions: Do all problems on separate paper. Show work or explain clearly. If you are basing your solution on a formula, state the formula you are using. Evaluate answers. Do not write an answer without support. Each question is worth 4 points. many different arrangemen e letters in the word EE are embers. In how many ways can the President Vice-President, ese positi be held by amer 3. A group of 22 employees se cts peop e to serve on a negotiating col be chosen? many 4-digit codes can 67 Id giff the first digit canng d digits cannot repeat? 5. From a group of 10 soph mores shme a subset of 5 students is formed consisting of 3 sophom and's freshmen How many such combinations are 6. Given a set Inear points: A, , C, D, and E. How many distinct lines can be A true-fal htains 10 que low many differer true and the quiz will not have to answers nori false answers? 8 (Easier to first calculate how many samples have no defective items.) 9. Use Pascal's triangle to expand the expression (x - y)5.This assignment is a basic introduction to combinatorics and probability. Before you begin, you will need to do some independent research. Do not attempt the problems without first looking up the following topics and taking some notes for yourself. You can use the textbook (primarily Chapter 9) and you can also do research online. Please let me know if you have any questions as you progress through the project, especially if are not sure how to interpret a problem. Topics: . Meaning of n! (n factorial) . Basic Counting Principal (or Multiplication Rule) . Definition of permutation . Definition of combination . The formula for ner . The formula for ncr, which is also represented as () . Number of arrangements of n distinct objects in a row . Number of arrangements of n distinct objects in a circle . Number of ways we can arrange n objects where r, are identical, 72 are identical, ..., and rx are identical. . Pascal's triangle . Number of subsets in a set with n elements . What is a sample space? . What is the definition of simple probability? Between what two values does probability lie? . What are mutually exclusive events? . What is the probability of event A or event B, if the events are mutually exclusive? What are independent events? . What is the probability of event A and event B, if the events are independent