Permutation or Combination?

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Vikia2009

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I'm having a little difficulty on this problem:
"In advertising a beach condo near Destin, Florida, a property owner can specify (1) whether or not pets are allowed, (2) whether the rent is based on off-season, during summer season, or during spring break, (3) whether or not children under 12 are allowed, (4) whether the minimum stay is 4, 7, or 10 days, and (5) whether or not is beach front. How many different versions of the ad can be generated?"
I thought version was just another word for combination, but if that is the case how do I figure out which would be n and which would be r for the equation :
(n r) n!/r!(n-r)!
 
Vikia2009 said:
I'm having a little difficulty on this problem:
"In advertising a beach condo near Destin, Florida, a property owner can specify (1) whether or not pets are allowed, (2) whether the rent is based on off-season, during summer season, or during spring break, (3) whether or not children under 12 are allowed, (4) whether the minimum stay is 4, 7, or 10 days, and (5) whether or not is beach front. How many different versions of the ad can be generated?"
I thought version was just another word for combination, but if that is the case how do I figure out which would be n and which would be r for the equation :
(n r) n!/r!(n-r)!
Click to expand...
Don't over-think this. Recall the first things you learned, like "how many license plates can be made, under [these] conditions?" You figured out the number of slots (such as characters on the license plate) and the number of options per slot (such as 26 for the number of letters and 10 for the number of numerals), and then you multiplied.

In this case, you have:

. . . . .[pets: yes/no] [rent: off/summer/spring] [children: yes/no] [days: 4/7/10] [beach: yes/no]

How many slots are there? How many options are there for each slot? Then how many different combinations can you make? ;)
 
stapel said:
Don't over-think this. Recall the first things you learned, like "how many license plates can be made, under [these] conditions?" You figured out the number of slots (such as characters on the license plate) and the number of options per slot (such as 26 for the number of letters and 10 for the number of numerals), and then you multiplied.

In this case, you have:

. . . . .[pets: yes/no] [rent: off/summer/spring] [children: yes/no] [days: 4/7/10] [beach: yes/no]

How many slots are there? How many options are there for each slot? Then how many different combinations can you make? ;)
Click to expand...

So there are 5 slots with 12 different options.
And to use the formula, I would have n=12 and r=5??
 
I wouldn't use that formula at all because all 12 "options" don't apply to all 5 "slots". I would use the more basic concept, the "fundamental principle of counting": If one thing can happen in m ways and another can happen, independently of the first, in n ways, then they can happen together in mn ways.

It's easy to extend that to three, four, or five things- multiply together the number of ways each can happen.

Here, you have one thing that can happen in 2 ways, another that can happen in 3 ways, a third that can happen in 2 ways, a fourth that can happen in 3 ways, and a fifth that can happen in 2 ways.
 
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