- - 1. Consider lists made from the letters C, O, M, P, U, T, E,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
- - 1. Consider lists made from the letters C, O, M, P, U, T, E, R. (a) How many lists of length 5 are there if repetition is allowed? (b) How many lists of length 5 are there if repetition is not allowed? (c) How many lists of length 4 are there that begin with the letter P if repetition is allowed? (d) How many lists of length 4 are there that do not begin with the letter P if repetition is not allowed? (e) How many lists of length 3 are there if repetition is allowed and the list must contain the letter C? - (f) How many lists of length 3 are there if repetition is not allowed and the list must contain the letter C? (Use MP/AP/SP) [4P] 2. How many integers between 1 and 1000 are divisible by 5? How many are not? (Use common sense) [1P] 3. A recent survey of European households revealed that 97% have at least one DVD-player, 96% have a cell phone, and 93% have a cell phone and at least one DVD-player. What percentage of households in the European Union have neither a cell phone nor a DVD-player? (Use IEP) [1P] 4. How many ways are there to select a first-prize winner, a second-prize winner, and a third- prize winner from among 250 students who have entered a campus-wide contest? (Use P/C) [1P] 5. How many different committees of three students can be formed from a group of five students? (Use P/C) [1P] 6. True or False? According to the Pigeonhole Principle, if we have n marbles and k boxes, then each box can have at most (7) marbles. [1P] 7. Consider a random group of 1,000 people. At least how many people were born in the same month? (Use DP/PP) [1P] 8. Students can score on the final exam anywhere from zero to 100 points. How many students need to take the exam so that it is guaranteed that at least two students have the exact same score? (Use DP/PP; watch out: how many different scores are there?) [1P] 9. Suppose students can earn one out of the five letter grades A, B, C, D, and F. How many students must a class have so that at least six of them will receive the same grade? (Use DP/PP) [1P] - - 1. Consider lists made from the letters C, O, M, P, U, T, E, R. (a) How many lists of length 5 are there if repetition is allowed? (b) How many lists of length 5 are there if repetition is not allowed? (c) How many lists of length 4 are there that begin with the letter P if repetition is allowed? (d) How many lists of length 4 are there that do not begin with the letter P if repetition is not allowed? (e) How many lists of length 3 are there if repetition is allowed and the list must contain the letter C? - (f) How many lists of length 3 are there if repetition is not allowed and the list must contain the letter C? (Use MP/AP/SP) [4P] 2. How many integers between 1 and 1000 are divisible by 5? How many are not? (Use common sense) [1P] 3. A recent survey of European households revealed that 97% have at least one DVD-player, 96% have a cell phone, and 93% have a cell phone and at least one DVD-player. What percentage of households in the European Union have neither a cell phone nor a DVD-player? (Use IEP) [1P] 4. How many ways are there to select a first-prize winner, a second-prize winner, and a third- prize winner from among 250 students who have entered a campus-wide contest? (Use P/C) [1P] 5. How many different committees of three students can be formed from a group of five students? (Use P/C) [1P] 6. True or False? According to the Pigeonhole Principle, if we have n marbles and k boxes, then each box can have at most (7) marbles. [1P] 7. Consider a random group of 1,000 people. At least how many people were born in the same month? (Use DP/PP) [1P] 8. Students can score on the final exam anywhere from zero to 100 points. How many students need to take the exam so that it is guaranteed that at least two students have the exact same score? (Use DP/PP; watch out: how many different scores are there?) [1P] 9. Suppose students can earn one out of the five letter grades A, B, C, D, and F. How many students must a class have so that at least six of them will receive the same grade? (Use DP/PP) [1P]
Expert Answer:
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
Students also viewed these mathematics questions
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
If the protein produced full length antibody, what would be the next step after centrifugation?
-
Historically, warranty expenditures have been equal to 4% of sales. Total sales for the year were $750,000. Actual warranty repairs made during the year totaled $37,400. Make the necessary summary...
-
Find the average rate of change of f(x) = 3x - 5 from x = 0 to x = 4.
-
A change in which the temperature of the system remains unchanged is called a/an (a) Irreversible change (b) Adiabatic change (c) Reversible change (d) Isothermal change.
-
On December 1, 2017, Rodriguez Distributing Company had the following account balances. During December, the company completed the following summary transactions. Dec. 6 Paid $1,600 for salaries and...
-
On 28 April 20X2, Peele Realty purchased land and building for $6.55 million and $4.69 million, respectively. The company uses the revaluation model for the land and building. Assume that the land is...
-
Portions of the payroll register for Barney's Bagels for the week ended July 15 are shown below. The SUTA tax rate is 5.4%, and the FUTA tax rate is 0.8%, both of which are levied on the first $7,000...
-
Let G = (N,A) be an undirected graph. (a) Suppose the arcs of G have with nonnegative weights. Explain how you could modify Dijkstra's algorithm (not G) to find a shortest path from a designated node...
-
True or False. The normal modes can also be called principal modes.
-
What is the difference between a general transfer function and a frequency transfer function?
-
How many degenerate modes can a vibrating system have?
-
What is a degenerate system? Give two examples of physical systems that are degenerate.
-
How can we make a system vibrate in one of its natural modes?
-
Explain the relationship between inflation and interest rate movements. Are they positively related? Does this finding support the loanable fund's theory? Does it support Fishers equation?
-
A 6-lb shell moving with a velocity ?? v0k explodes at point D into three fragments which hit the vertical wall at the points indicated. Fragments A, B, and C hit the wall 0.010 s, 0.018 s, and 0.012...
-
For R = {s, t, x, y}, define + and , making R into a ring, by Table 14.5(a) for + and by the partial table for + in Table 14.5(b). (a) Using the associative and distributive laws, determine the...
-
(a) Find a dual graph for each of the two planar graphs and the one planar multi graph in Fig. 11.72. (b) Does the dual for the multigraph in part (c) have any pendant vertices? If not, does this...
-
For the relation R in Example 7.13, let f: Z+ R where f(n) = n. (a) Find three elements f1, f2, f3 F such that f1 R f and f R f1, for all 1 i 3. (b) Find three elements g1, g2, g3 F such that g1...
-
A flywheel is mounted on a vertical shaft, as shown in Fig. 2.76. The shaft has a diameter \(d\) and length \(l\) and is fixed at both ends. The flywheel has a weight of \(W\) and a radius of...
-
A TV antenna tower is braced by four cables, as shown in Fig. 2.77. Each cable is under tension and is made of steel with a cross-sectional area of \(322 \mathrm{~mm}^{2}\). The antenna tower can be...
-
A building frame is modeled by four identical steel columns, each of weight \(w\), and a rigid floor of weight \(W\), as shown in Fig. 2.79. The columns are fixed at the ground and have a bending...
Study smarter with the SolutionInn App