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Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that both begin and end with consonants?

Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that both begin and end with consonants?

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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ting Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that both begin and end with consonants?
Transcribed Image Text:ting Taking into account identical letters, how many ways are there to arrange the word PARVAMONSTRA that both begin and end with consonants?
4. (20) Taking into account identical letters, how many ways are there to arrange the word HUDSONICUS that begin with a vowel or end with a consonant? Any path to the right answer gets full credit. Deduct only 1 point for things like off-by-one errors, even if there is more than one. The consonants are H, D, S, N and C. S is used twice, all others are used once. For vowels, U is used twice, O and I are used once. ● 2121 Cases that end with an S look like (HUDSONICU)S. 9 letters and two U's, for = 181,440. Cases that end with a different consonant look like (HUDSONIUS)C. 9 letters, two S's, and two U's, for 91 212! = 90,720. There are four sets of these. We're going to need to handle inclusion/exclusion. ● ● Cases that begin with a U look like U(HDSONICUS). 9 letters and two S's, for = 181,440. Cases that begin with a different vowel look like O(HUDSNICUS). 9 letters, two S's, and two U's, for 9! = 90,720. There are two sets of these. ● Cases that begin with a U and end with an S look like U(HDSONICU)S. 8! = 40,320. Cases that begin with a U and end with another consonant look like U(HDSONIUS)C. are four sets of these. Cases that begin with another vowel and end with an S look like O(HUDSNICU)S. two sets of these. Cases that begin with another vowel and end with another consonant look like O(HUDSNIUS)C. = 10,080. There are eight sets of these. 2121 So we have 181,440 x 2 + 90,720 x 6-40,320-20,160 x 6-10,080 x8= +544,320-40,320-120,960-80,640 665, 280. 362,880 20,160. There 20,160. There are
Transcribed Image Text:4. (20) Taking into account identical letters, how many ways are there to arrange the word HUDSONICUS that begin with a vowel or end with a consonant? Any path to the right answer gets full credit. Deduct only 1 point for things like off-by-one errors, even if there is more than one. The consonants are H, D, S, N and C. S is used twice, all others are used once. For vowels, U is used twice, O and I are used once. ● 2121 Cases that end with an S look like (HUDSONICU)S. 9 letters and two U's, for = 181,440. Cases that end with a different consonant look like (HUDSONIUS)C. 9 letters, two S's, and two U's, for 91 212! = 90,720. There are four sets of these. We're going to need to handle inclusion/exclusion. ● ● Cases that begin with a U look like U(HDSONICUS). 9 letters and two S's, for = 181,440. Cases that begin with a different vowel look like O(HUDSNICUS). 9 letters, two S's, and two U's, for 9! = 90,720. There are two sets of these. ● Cases that begin with a U and end with an S look like U(HDSONICU)S. 8! = 40,320. Cases that begin with a U and end with another consonant look like U(HDSONIUS)C. are four sets of these. Cases that begin with another vowel and end with an S look like O(HUDSNICU)S. two sets of these. Cases that begin with another vowel and end with another consonant look like O(HUDSNIUS)C. = 10,080. There are eight sets of these. 2121 So we have 181,440 x 2 + 90,720 x 6-40,320-20,160 x 6-10,080 x8= +544,320-40,320-120,960-80,640 665, 280. 362,880 20,160. There 20,160. There are
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