Permutation, Combination, and Repetition

Date: 11/25/98 at 14:43:33
From: nelly
Subject: Permutations

1. What is a permutation with repetition, and no repetition?
2. What is a combination with repetition, and no repetition?

 thank you, Nelly

Date: 11/25/98 at 18:52:06
From: Doctor Schwa
Subject: Re: Permutations

1. What is a permutation with repetition, and no repetition?

Permutation means putting some objects in order, and repetition means 
you're allowed to use the same ones twice. For instance, if you have 
five objects (a, b, c, d, e) and you want to take three of them, (say, 
president, VP, treasurer of your club), you can do it as

abc, acb, bac, bca, cab, cba
abd, adb, bad, bda, dab, dba 
abe, aeb, .... 

you get the idea.

There should be 10 rows of 6 if you keep following the pattern that I 
started. A total of 60, 5*4*3 (you start with 5 because you have 5 
objects to choose from for what goes first, and you then have 4 choices 
for who goes next, and 3 choices for who goes last).

If you allow repetition, then in addition to these examples, you also 
have things like

aab, aba, baa
aac, aca, caa
or even just aaa ...

now there are a total of 125, 5*5*5, since you have 5 choices for which 
letter goes in each spot.

2. What is a combination with repetition, and no repetition?

It's the same idea, only now the order you choose them in doesn't 
matter. Imagine you're choosing 3 of 5 people to give a free pizza
to - it doesn't matter who gets the free pizza first. So all the things 
I listed on the same line in the examples above would now just count as 
one thing.

With/without repetition still means the same as before.

I also highly recommend looking in the Dr. Math FAQ at

  http://mathforum.org/dr.math/faq/   

because it says a lot more about permutations and combinations.

- Doctor Schwa, The Math Forum
  http://mathforum.org/dr.math/