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We want to build 8 letter "words" using only the first n=10 letters of the alphabet. For example, if n-5 we can use the first 5 letters, (a, b, c, d, e) (Recall, words are just strings of letters, not necessarily actual English words.) a. How many of these words are there total? 10^8 b. How many of these words contain no repeated letters? 1814400 c. How many of these words start with the sub-word "ade"? 10^5 d. How many of these words either start with "ade" or end with "be" or both? 10^5+10^6- e. How many of the words containing no repeats also do not contain the sub-word "bed"? 1814400-33

We want to build 8 letter "words" using only the first n=10 letters of the alphabet. For example, if n-5 we can use the first 5 letters, (a, b, c, d, e) (Recall, words are just strings of letters, not necessarily actual English words.) a. How many of these words are there total? 10^8 b. How many of these words contain no repeated letters? 1814400 c. How many of these words start with the sub-word "ade"? 10^5 d. How many of these words either start with "ade" or end with "be" or both? 10^5+10^6- e. How many of the words containing no repeats also do not contain the sub-word "bed"? 1814400-33

Advanced Engineering Mathematics
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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We want to build 8 letter "words" using only the first r= 10 letters of the alphabet. For example, if n 5 we can use the first 5 letters, (a, b, c, d, e) (Recall, words are just strings of letters, not necessarily actual English words.) a. How many of these words are there total? 10^8 b. How many of these words contain no repeated letters? 1814400 c. How many of these words start with the sub-word "ade"? 10^5 d. How many of these words either start with "ade" or end with "be" or both? 10^5+10^6- e. How many of the words containing no repeats also do not contain the sub-word "bed"? 1814400-33
Transcribed Image Text:We want to build 8 letter "words" using only the first r= 10 letters of the alphabet. For example, if n 5 we can use the first 5 letters, (a, b, c, d, e) (Recall, words are just strings of letters, not necessarily actual English words.) a. How many of these words are there total? 10^8 b. How many of these words contain no repeated letters? 1814400 c. How many of these words start with the sub-word "ade"? 10^5 d. How many of these words either start with "ade" or end with "be" or both? 10^5+10^6- e. How many of the words containing no repeats also do not contain the sub-word "bed"? 1814400-33
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