Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Permutations of Indistinguishable Objects


Date: 09/21/2000 at 18:12:33
From: Candice
Subject: Permutations of Indistinguishable Objects and Multiplication 
Principle

Hi Dr. Math, 

I'm hoping you can help me out with two questions.

1. A forester selects four pink and four white dogwoods. The trees are 
to be planted in row. If a tree is distinguished by color only, in how 
many ways can the eight dogwoods be planted? How many of these 
arrangements have at least two trees of the same color side by side?

I found the number of possibilities to be 576 (4x3x2x1x4x3x2x1), but 
I don't know how to find the second answer.

2. A study is being designed to investigate the effect of polymer 
type, temperature, radiation dose, radiation dose rate, and pH on the 
ability to remove trace quantities of benzene from water. There are 
2 polymer types (A and B), 3 temperatures (high, medium, low), 3 
radiation doses, 3 radiation dose rates and 3 pH levels (acidic, 
basic, neutral).

a) If each experimental condition is to replicated 5 times, how many 
experimental runs must be made?

b) How many runs are made with polymer B at high or medium temperature 
and low pH?

For a) I got 810 - number of possible conditions x 5. For b) I got 
1x2x1x3x3 = 18. Is this correct?

Thank you in advance.


Date: 09/21/2000 at 19:18:34
From: Doctor Anthony
Subject: Re: Permutations of Indistinguishable Objects and 
Multiplication Principle

>If a tree is distinguished by color only, in how 
>many ways can the eight dogwoods be planted?  

The number of arrangements is  8!/[4!4!] = C(8,4) = 70

>How many of these 
>arrangements have at least two trees of the same color side by side?

It is best to find the number of ways with no two of the same colour 
side by side, and subtract this number from 70.

Suppose we place the 4 white trees in a row with spaces between them 
and then place the pink trees as shown:

    P *  P  *  P  *  P  * 
or
      *  P  *  P  *  P  *  P

and these are the only two ways that we have no two of the same colour 
side by side. So the number of ways with at least two side by side is 
68.


>2a) If each experimental condition is to replicated 5 times how many 
>experimental runs must be made?

 5 x 2 x 3 x 3 x 3 x 3 = 810

>2b) How many runs are made with polymer B at high or medium 
>temperature and low pH?

 5 x 1 x 2 x 3 x 3 x 1 = 90 

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Permutations and Combinations

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/