A company has 10 different warehouses for storing their inventory. They will be storing 100 identical crates of widgets in the 10 warehouses. (a) How many ways are there for the company to distribute the crates of widgets among the warehouses? (b) How many ways are there for the company to distribute the crates of widgets among the warehouses if at least 5 crates must be stored at each warehouse?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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This is a discrete math (counting techniques) problem. Please explain clearly, no cursive writing.

 

A company has 10 different warehouses for storing their inventory. They will be storing 100
identical crates of widgets in the 10 warehouses.
(a) How many ways are there for the company to distribute the crates of widgets among the
warehouses?
(b) How many ways are there for the company to distribute the crates of widgets among the
warehouses if at least 5 crates must be stored at each warehouse?
(c) How many ways are there for the company to distribute the crates of widgets among the
warehouses if at most 50 crates can be stored at any one warehouse?
(d) How many ways are there for the company to distribute the crates of widgets among the
warehouses if at most 40 crates can be stored at any one warehouse?
Transcribed Image Text:A company has 10 different warehouses for storing their inventory. They will be storing 100 identical crates of widgets in the 10 warehouses. (a) How many ways are there for the company to distribute the crates of widgets among the warehouses? (b) How many ways are there for the company to distribute the crates of widgets among the warehouses if at least 5 crates must be stored at each warehouse? (c) How many ways are there for the company to distribute the crates of widgets among the warehouses if at most 50 crates can be stored at any one warehouse? (d) How many ways are there for the company to distribute the crates of widgets among the warehouses if at most 40 crates can be stored at any one warehouse?
Additional Instructions
For the exercises that ask you to answer "How many ...", express your results as a combinatorial
formula, calculate the integer value that answers the question, and provide a short justification of
your formula choice.
Transcribed Image Text:Additional Instructions For the exercises that ask you to answer "How many ...", express your results as a combinatorial formula, calculate the integer value that answers the question, and provide a short justification of your formula choice.
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