Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and... Problem 1.2P: How many outcome sequences are possible ten a die is rolled four times, where we say, for instance,... Problem 1.3P: Twenty workers are to be assigned to 20 different jobs, one to each job. How many different... Problem 1.4P: John, Jim, Jay, and Jack have formed a band consisting of 4 instruments if each of the boys can play... Problem 1.5P: For years, telephone area codes in the United States and Canada consisted of a sequence of three... Problem 1.6P: A well-known nursery rhyme starts as follows: As I was going to St. Ives I met a man with 7 wives.... Problem 1.7P: a. In how many ways can 3 boys and 3 girls sit in a row? b. In how many ways can 3 boys and 3 girls... Problem 1.8P: When all letters are used, how many different letter arrangements can be made from the letters a.... 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Problem 1.18P: A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How... Problem 1.19P: Seven different gifts are to be distributed among 10 children. How many distinct results are... Problem 1.20P: A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from... Problem 1.21P: From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How... Problem 1.22P: A person has 8 friends, of whom S will be invited to a party. a. How many choices are there if 2 of... Problem 1.23P: Consider the grid of points shown at the top of the next column. Suppose that, starting at the point... Problem 1.24P: In Problem 23, how many different paths are there from A to B that go through the point circled in... Problem 1.25P: A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3... Problem 1.26P: Show k=0n(nk)2k=3n Simplify k=0n(nk)xk Problem 1.27P: Expand (3x2+y)5. Problem 1.28P: The game of bridge is played by 4 players, each of w1om is dealt 13 cards. How many bridge deals are... Problem 1.29P: Expand (x1+2x2+3x3)4. Problem 1.30P: If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions... Problem 1.31P: If 8 new teachers are to be divided among 4 schools, how many divisions are possible? What if each... Problem 1.32P: Ten weight lifters are competing in a team weight-lifting contest. Of the lifters, 3 are from the... Problem 1.33P: Delegates from 10 countries, including Russia, France, England, and the United States, are to be... Problem 1.34P: If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? How... Problem 1.35P: An elevator starts at the basement with 8 people (not including the elevator operator) and... 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Problem 1.8TE: Prove that (n+mr)=(n0)(mr)+(n1)(mr1)+...+(nr)(m0) Hint: Consider a group of n men and m women. How... Problem 1.9TE: Use Theoretical Exercise 8 I to prove that (2nn)=k=0n(nk)2 Problem 1.10TE: From a group of n people, suppose that we want to choose a committee of k,kn, one of whom is to be... Problem 1.11TE: The following identity is known as Fermats combinatorial identity:(nk)=i=kn(i1k1)nk Give a... Problem 1.12TE: Consider the following combinatorial identity: k=0nk(nk)=n2n1 a. Present a combinatorial argument... Problem 1.13TE: Show that, for n0 ,i=0n(1)i(ni)=0 Hint: Use the binomial theorem. Problem 1.14TE: From a set of n people, a committee of size j is to be chosen, and from this committee, a... Problem 1.15TE: Let Hn(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1xin... Problem 1.16TE: Consider a tournament of n contestants in which the outcome is an ordering of these contestants,... 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![**Quality Control Analysis of Ceramic Tiles**
A manufacturing company performs a quality control analysis on the ceramic tiles it produces. Suppose a batch of 15 tiles has 8 defective tiles. If 6 tiles are sampled at random, what is the probability that exactly 1 of the sampled tiles is defective?
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**Question:**
How many ways can 6 tiles be selected from 15 tiles?
- [ ] ways
*(Type a whole number.)*
*(This problem involves combinatorial analysis to determine the number of possible ways to select a subset of tiles from the total. Calculating the probability that only one of the tiles selected is defective further involves understanding combinations.)*](https://content.bartleby.com/qna-images/question/1cdef31d-0fd6-49ca-a823-5c1cf3cbca2c/3acaa68a-cf67-4c8e-addf-b798ac1d87d8/pkwva6l_processed.jpeg)
