Solutions from a student (dragged) 28

# Solutions from a student (dragged) 28 - To count the number...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: To count the number of solutions to this equation consider the number of equations with x i ≥ 1 and ∑ n i =1 x i = ˆ k , which is ˆ k- 1 n- 1 so to calculate the number of equations to the requested problem we add these up for all ˆ k < k . The number of solutions is given by k ˆ k = n ˆ k- 1 n- 1 with k > n. Chapter 1: Self-Test Problems and Exercises Problem 1 (counting arrangements of letters) Part (a): Consider the pair of A with B as one object. Now there are two orderings of this “fused” object i.e. AB and BA . The remaining letters can be placed in 4! orderings and once an ordering is specified the fused A/B block can be in any of the five locations around the permutation of the letters CDEF . Thus we have 2 · 4! · 5 = 240 total orderings. Part (b): We want to enforce that A must be before B . Lets begin to construct a valid sequence of characters by first placing the other letters CDEF , which can be done in 4! = 24 possible ways. Now consider an arbitrary permutation ofpossible ways....
View Full Document

## This note was uploaded on 02/25/2011 for the course STAT 418 taught by Professor G.jogeshbabu during the Winter '08 term at Penn State.

Ask a homework question - tutors are online