A classmate was assigned the task of calculating the number of ten letter words that have a minimum of three A's. He handed you the following calculation process: "Starting off, I chose three different spots for each A. Since there are ten positions, there are (10 choose 3) ways for this to work. Every other spot can have any letter it wants, so with seven spots and twenty-six letters there are 267 choices for the spots. Given this information, I am left with (10 choose 3)*267 words that have a minimum of three A's." However, you know this is wrong because it overcounts the number of words. Identify the errors that your classmate made. (This is a combinatorics and graph theory math question)
A classmate was assigned the task of calculating the number of ten letter words that have a minimum of three A's. He handed you the following calculation process: "Starting off, I chose three different spots for each A. Since there are ten positions, there are (10 choose 3) ways for this to work. Every other spot can have any letter it wants, so with seven spots and twenty-six letters there are 267 choices for the spots. Given this information, I am left with (10 choose 3)*267 words that have a minimum of three A's." However, you know this is wrong because it overcounts the number of words. Identify the errors that your classmate made. (This is a combinatorics and graph theory math question)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A classmate was assigned the task of calculating the number of ten letter words that have a minimum of three A's. He handed you the following calculation process:
"Starting off, I chose three different spots for each A. Since there are ten positions, there are (10 choose 3) ways for this to work. Every other spot can have any letter it wants, so with seven spots and twenty-six letters there are 267 choices for the spots. Given this information, I am left with (10 choose 3)*267 words that have a minimum of three A's."
However, you know this is wrong because it overcounts the number of words. Identify the errors that your classmate made.
(This is a combinatorics and graph theory math question)
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