Several have written to this thread and I believe there has been some
misleading information passed along and intermixed with correct
information.
On Sun, 29 Apr 2001 11:26:11 -0400 "Zina Taran"
<[EMAIL PROTECTED]> writes:
> I believe, the thrust of the "fries" reply was the overcount in the
> 5*4*3*..... response rather than an expression of culinary
> preferences.
Multiplying 5*4*3... is the kind of multiplication used when determining
the 'number of permutations'.
I seem to remember the question asked for "number of combinations".
The first step to obtaining the answer is to be sure you understand what
you are 'counting.'
If PERMUTATIONS -
If you consider a "hamburger with lettuce and mayo" to be different than
a "hamburger with mayo and lettuce", then you want to count the "number
of permutations." Permutations involve the concept of "order" [rather it
be 'the order in which you listed the condiments when placing the order'
or 'the order in which the condiments are placed on your burger'] as an
integral part of the problem. As applied to this particular problem,
there were 5 condiments - for the first condiment selected there are 5
choices, for the second condiment selected there would be 4 choices
available, and so on. Then by multiplying, you find the number of
possibilities. I seriously doubt that you are interested in counting the
"number of permutations."
If COMBINATIONS -
If what you want to know is "how many different combinations of
condiments can be ordered", with no regards to an "order" concept, then
you are interested in counting the "number of combinations". It is this
concept that I would think answers the question asked.
One way to approach this is to look at and determine the count for each
case, then find the total. [This approach was suggested in an earlier
e-mail.]
Five (5) condiments to choose from -
1) find the number of ways you can select exactly zero (0) condiments -
there is 1,
2) find the number of ways you can select exactly one (1) condiment -
there are 5,
3) find the number of ways you can select exactly two (2) condiments -
there are 10,
4) find the number of ways you can select exactly three (3) condiments -
there are 10,
5) find the number of ways you can select exactly four (4) condiments -
there are 5,
6) find the number of ways you can select exactly five (5) condiments -
there are 1,
I'll leave it to you to find each of them.
Answer: 1+5+10+10+5+1 = 32 different possible combinations of condiments
can be ordered.
If you are not interested in all the cases individually, there is a
shorter way. Think of each different condiment that you can order, say
pickles - you have 2 choices - 'order it' or 'don't order it'. The same
two (2) options are available for each of the other condiments - catsup,
mayo, lettuce, etc. [even for the fries and onion rings, if you want them
included as a condiment on your burger. :-} ]
Now what you have is a special case of the basic "Multiplication Rule".
Two (2) choices for each condiment, 2*2*2* ... *2, using 'n' 2's, or
2**n. Thus, if you have 5 condiments to choose from, there are 2**5 =
32 different combinations of condiments can be ordered for your
hamburger.
I hope this helps.
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Robert R. & Barbara S. Johnson
E-mail: [EMAIL PROTECTED]
Post: 84 West Lake Rd., Branchport, NY 14418
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