**Small Monster Research and Marmoset Taxonomy**After watching a charming online video, a Small Monster collector has embarked on a new journey as a Small Monster researcher. This endeavor focuses on creating a taxonomic classification that redefines marmosets not as conventional animals, but as Small Monsters. To support this intriguing hypothesis, the researcher is revisiting the biological family of marmosets.### ExerciseConsider the word "CALLITRICHIDAE" and tackle the following questions while accounting for identical letters:a. How many unique arrangements of the word CALLITRICHIDAE are possible?b. How many arrangements of the word CALLITRICHIDAE start or end with vowels?c. How many arrangements of the word CALLITRICHIDAE include the substring "LITERAL"?

a) Given word is CALLITRICHIDAE Total number of letters in this word is 14. Number of times Letter C repeats =2 Number of times Letter L repeats =2 Number of times Letter I repeats =3 Number of times Letter A repeats =2 So, the given word can be arranged in 14!3!2!2!2! ways.b) vowels in the word CALLITRICHIDAE are A,A,I,I,I,E so, total number of vowels in the given word is 6 Number of words that start with vowels =6×13!2!3!2!2! Number of words that ends with vowels =6×13!2!3!2!2! Number of words that start and ends with vowels =6×5×12!2!3!2!2! So, Number of words that start or ends with vowels= 6×13!2!3!2!2!+6×13!2!3!2!2!-6×5×12!2!3!2!2! ==6×12!2!3!2!2!(13+13-5)=6×12!×212!3!2!2! c) Now, we will count word LITERAL as 1 letter. The remaining letters are C,A,I,C,H,I,D (i.e. 7 letters) So , the number of ways the word CALLITRICHIDAE can be arranged containing substring LITERAL is 8!2!2!

Math

Advanced Math

2. After catching sight of a particularly adorable online video, the Small Monster collector has begun a second career as a Small Monster researcher, intending to develop a taxonomic argument that marmosets are not in fact conventional animals, but are in fact Small Monsters. As a warm-up to their argument, they are reminding themselves of the biological family to which marmosets belong. a. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE? b. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE that start or end with vowels? C. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE that contain the substring LITERAL?

2. After catching sight of a particularly adorable online video, the Small Monster collector has begun a second career as a Small Monster researcher, intending to develop a taxonomic argument that marmosets are not in fact conventional animals, but are in fact Small Monsters. As a warm-up to their argument, they are reminding themselves of the biological family to which marmosets belong. a. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE? b. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE that start or end with vowels? C. Taking into account identical letters, how many ways can the researcher arrange the word CALLITRICHIDAE that contain the substring LITERAL?

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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**Small Monster Research and Marmoset Taxonomy**

After watching a charming online video, a Small Monster collector has embarked on a new journey as a Small Monster researcher. This endeavor focuses on creating a taxonomic classification that redefines marmosets not as conventional animals, but as Small Monsters. To support this intriguing hypothesis, the researcher is revisiting the biological family of marmosets.

### Exercise

Consider the word "CALLITRICHIDAE" and tackle the following questions while accounting for identical letters:

a. How many unique arrangements of the word CALLITRICHIDAE are possible?

b. How many arrangements of the word CALLITRICHIDAE start or end with vowels?

c. How many arrangements of the word CALLITRICHIDAE include the substring "LITERAL"?

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