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.... Problem 1.9P: A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts... Problem 1.10P: In how many ways can 8 people be seated in a row if a. there are no restrictions on the seating... Problem 1.11P: In how many ways can 3 novels. 2 mathematics books, and 1 chemistry book be arranged on a bookshelf... Problem 1.12P: How many 3 digit numbers zyz, with x, y, z all ranging from 0 to9 have at least 2 of their digits... Problem 1.13P: How many different letter permutations, of any length, can be made using the letters M 0 T T 0. (For... Problem 1.14P: Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to... Problem 1.15P: Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take... Problem 1.16P: How many 5-card poker hands are there? Problem 1.17P: A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women... 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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![5. Consider a trinary communication channel [STAR 1979] whose channel diagram
is shown in Figure 1.P.6. For i = 1, 2, 3 let T, denote the event "digit i is trans-
mitted" and let R, denote the event "digit i is received." Assume that a 3 is
transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1.
If a 1 has been received, what is the expression for the probability that a 1 was
sent? Derive an expression for the probability of a transmission error.
P(R1IT1) =1-oa
T1
R1
a/2
a /2
B/2
1-B
T2
R2
B/2
Y/2
Y/2
1-y
T3
R3
Figure 1.P.6. A trinary communication channel: channel diagram](https://content.bartleby.com/qna-images/question/653a6d11-6512-400f-875b-a9bd6bc11d13/40f7cf96-edae-4a16-8160-4c78ae5b2033/jxtwmy_processed.jpeg)
