discreat math probs MTH 220 Section 1: Problem Set 1 (take home component) Tenta
ID: 3111875 • Letter: D
Question
discreat math probs
MTH 220 Section 1: Problem Set 1 (take home component) Tentative due date: Monday, September 25th Provide solutions to the following exercises on your own paper: 1: A math professor has 4 graph theory books; 4 combinatorics books; and 6 set theory books. How many ways can these books be placed on a shelf if books are organized by their topics? 2: A bowl contains 5 red balls and 10 blue balls. A woman selects 4 balls at random from the bowl. How many different selections are possible if at least 3 balls must be blue? 3: Without constructing Pascal's triangle, what is the binomial expansion for the expression (x+1 Justify your response using combinatorics. 4: How many anagrams can be created from the word 'metamorphosis' if the new words do not need to be meaningful? 5: 15 indistinguishable glass orbs are arranged in a row. How many different ways are there to partition the glass orbs into 5 sets? 6: Prove, via induction: For all integers n>0 346+94 +3n =-n(n +1)Explanation / Answer
Solution:
SInce professor has 4 graph theory books therefore arrangement by topic = 4!
and 4 combinatorics Books therefore arrangement by topic = 4!
and 6 set theory books therefore arrangement by topic = 6!
therefore total number of books different type = 1+1+1 =3!
Now
4 !* 4! * 6* 3! = 2488320 ways
books are organized by their topic (same kinds are next to each other) =Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.