Combinations and Permutations : Ways to paint the 10 identical rooms 5 colors; Find the egf for the number of ways to distribute r distinct objects into n boxes.

Exercise #1 A) How many ways are there to paint the 10 identical rooms in a hotel with five colors if at most three rooms can be painted green, at most three painted blue, at most three red, and no constraint on the other two colors, black and white. B) Show that ...is the generating function for the number of ways a sum o ...continues

Evaluate the sum using generating functions.

Evaluate the sum (using generating functions) A) 0+3+12+…+3n2. B) 4x3x2x1+5x4x3x2+…+n(n-1)(n-2)(n-3)

How many r-digit ternary sequences are there in which...

How many r-digit ternary sequences are there in which A) No digit occurs exactly twice? B) 0 and 1 each appear a positive even number of times?

Find an exponential generating function for the number of distributions of r distinct objects into n different boxes with exactly m nonempty boxes.

Find an exponential generating function for the number of distributions of r distinct objects into n different boxes with exactly m nonempty boxes.

Recurrence Relations : Lines and Planes; Savings and Interest; n-Digit Ternary Sequences

1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal. 2) Find and solve a recurrence relation for the number of infinite regions formed by n infinite lines drawn in the plane so that each pair of lines intersects at a different point. 3) Find and solve a ...continues

Recurrence Relations, Functional Equation, Generating Functions and N-Digit Ternary Sequences

1. Find a functional equation and solve it for sequence of generating functions whose coefficients satisfy (assume and =1): 1. 2. Find a recurrence relation and associated generating function for the number of n-digit ternary sequence that have the pattern "012" occurring for the first time at end of the sequence. ...continues

Find the perimeter of an octagon inscribed in a circle.

A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.

Business math problems

Complete the vertical and horizontal analysis of the comperative balance sheet for Miller's Model Ships. (See attached file for full problem description)

Corporate Finance : Interest Rate Formula K = R + [ (1.25 X (14 - R)] and Solving for Unknown Variables

I am working on corporate finance and figuring out interest rates. The problem has some of the givens, I need to find the value of the unidentified given. Other examples: 15% = R + [1.25 x (14% - R )] 16% = 9% + [1.10 x (k - 9%)] 15% = 10% + [b x (12.5% - 10%)]

Solve these problems using inclusion-exclusion approach.

Solve these problems using inclusion-exclusion approach. 1- Given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same? 2- How many integers solution of are there with: a. b. -10 3- How many secret codes can be made by assigning each letter of th ...continues