2. The planner in charge of raw materials operations at a well known beer-producing company needs to obtain 5 truckloads of fresh water. The five trucks available can go to any of 11 sources of water (mainly dams and reservoirs). The basic question is how many possible ways this can be achieved, using each truck once. The 11 sources all have different kinds of minerals in the water, so it is always important how many truckloads come from which source, but there are different conditions as follows. Find the number of ways in each case. You may leave your answer expressed in terms of binomials, factorials, integers raised to integer powers, or products and quotients of these, unless otherwise requested. (Important: make sure you explain what formulae you use, and why. (a) It does not matter which truck brings which kind of water, and any sources can be used by any number of trucks. Express your answer as a single integer. (b) It does not matter which truck brings which kind of water, but no source can be used by more than one truck. In this case, give the answer as a single integer. (c) The company needs to keep track of how far each truck goes, so two arrangements are counted as different if they send different trucks to any given source. Still, no source can be used by more than one truck.
2. The planner in charge of raw materials operations at a well known beer-producing company needs to obtain 5 truckloads of fresh water. The five trucks available can go to any of 11 sources of water (mainly dams and reservoirs). The basic question is how many possible ways this can be achieved, using each truck once. The 11 sources all have different kinds of minerals in the water, so it is always important how many truckloads come from which source, but there are different conditions as follows. Find the number of ways in each case. You may leave your answer expressed in terms of binomials, factorials, integers raised to integer powers, or products and quotients of these, unless otherwise requested. (Important: make sure you explain what formulae you use, and why. (a) It does not matter which truck brings which kind of water, and any sources can be used by any number of trucks. Express your answer as a single integer. (b) It does not matter which truck brings which kind of water, but no source can be used by more than one truck. In this case, give the answer as a single integer. (c) The company needs to keep track of how far each truck goes, so two arrangements are counted as different if they send different trucks to any given source. Still, no source can be used by more than one truck.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2. The planner in charge of raw materials operations at a well known beer-producing
company needs to obtain 5 truckloads of fresh water. The five trucks available can
go to any of 11 sources of water (mainly dams and reservoirs). The basic question is
how many possible ways this can be achieved, using each truck once. The 11 sources
all have different kinds of minerals in the water, so it is always important how many
truckloads come from which source, but there are different conditions as follows. Find
the number of ways in each case. You may leave your answer expressed in terms of
binomials, factorials, integers raised to integer powers, or products and quotients of
these, unless otherwise requested. (Important: make sure you explain what formulae you
use, and why.
(a) It does not matter which truck brings which kind of water, and any sources can be
used by any number of trucks. Express your answer as a single integer.
(b) It does not matter which truck brings which kind of water, but no source can be
used by more than one truck. In this case, give the answer as a single integer.
(c) The company needs to keep track of how far each truck goes, so two arrangements
are counted as different if they send different trucks to any given source. Still, no
source can be used by more than one truck.
(d) The conditions in (c) hold, but additionally the company needs to record the order
that the trucks return with the water. How many possible outcomes are there?
(e) The conditions in (a) hold, but additionally there is one of the sources that may only
be used at most twice due to lack of supply. (The other sources are unrestricted).
Express your answer as a single integer.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 13 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
