Discrete Mathematics Answers

prove that the largest possible number of leaves in an n-tree of height k in n^k

How many arrangements of six 0’s, five 1’s and four 2’s are there in which:
i) The first 0 precedes the first 1?
ii) The first 0 precedes the first 1, which precedes the first 2?

If the sum of divisors of n, that is (n) is equal to 2n, then n is called a perfect number.
Show that if n is an odd perfect number then n has at least three different prime
divisors.

Let E = {2, 4, 6, …}. Then prove that (E, +) is a semigroup, where + is usual addition.

Find the edge chromatic number of Kn, where n is a positive integer.

How many nonisothropic spanning trees does each of these simple graphs have?

a. K3 b. K4 c. K5

Situation:A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general population. A random sample of 90 students at a private high school is tested and and a mean SAT score of 1030 is obtained. The average score for public high school student is 1000 (σ= 200).
Question: Determine the 95 % confidence interval for the population mean, based on the sample mean.

What is the number of edges in a K^n?