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Perm & Comb

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Manager
Joined: 03 Sep 2005
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Perm & Comb [#permalink]  15 Sep 2005, 20:35
Can anyone please provide clarification as to when we should use the permutation formula and when we should use the combination formula? I'm so confused and I only have 3 days until my test!

I was trying to solve this problem:

The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

I used the combination solution for this because we are trying to find the number of combos for 2 slots out of 122 and 124 different options. However, the solution just 124^2-122^2. I don't understand. Please help!
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Manager
Joined: 15 Jul 2005
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[#permalink]  15 Sep 2005, 21:20
I think you may have over analyzed the problem!

It really asks how many more combinations are there if 124 characters are used, instead of 122. Since nothing is mentioned about repeating signs, we can assume repeating signs is allowed. 2 digits.

so for each digit 124 signs = 124*124
as opposed to 122 signs per digit = 122*122

which gives us 124^2-122^2
Manager
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[#permalink]  15 Sep 2005, 21:27
Use permutation when order is of importance, and combination when it isn't. For example, when you count abc different from bca, permutation should be kept in mind. On the same note, if knowing abc has been selected is of importance, combination should be kept in mind.

Hope this helps!
Manager
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[#permalink]  16 Sep 2005, 05:21
Overanalyzing is my middle name! Thanks for your input! If only I had your brain...

chets wrote:
Use permutation when order is of importance, and combination when it isn't. For example, when you count abc different from bca, permutation should be kept in mind. On the same note, if knowing abc has been selected is of importance, combination should be kept in mind.

Hope this helps!

_________________

Life is not measured by the number of breaths you take, but by the number of moments that take your breath away.

[#permalink] 16 Sep 2005, 05:21
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