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Combinatorics (permutation)

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Intern
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Joined: 30 Sep 2008
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Combinatorics (permutation) [#permalink]

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New post 13 Oct 2008, 09:44
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hi, I need help working out a type of permutation. EG I am using the 26 letters from the alphabet to create a 3 letter code where order matters. However, any letter can be repeated only twice. How many possible codes can I create?

If you need more clarity see the question below. The line in bold is where I got the question above from. If there is an easier way to ans the question below, please let me know. Thanks.

------------------------------------------------------------------

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

o 2,951
o 8,125
o 15,600
o 16,302
o 18,278

My shot at working this out.

1) There are 3 Code types A, BC, ABC
2) for A types there will be 26 codes
3) for BC types with diff letters there will be 650 codes (from permutation 26X25)
4) for BC types with same letters there will be 26 codes (eg AA, BB, CC)
5) for ABC types with diff letters there will 15600 codes (from permutation 26x25x24)
5) for ABC types with all same letters there will 26 codes (eg AAA, BBB, CCC)
6) for ABC types with 2 similar letters (eg AAB, BBA, CCB,) I am not sure how to work out

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Intern
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Joined: 30 Sep 2008
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Re: Combinatorics (permutation) [#permalink]

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New post 13 Oct 2008, 11:22
You are correct. I figured you can get E by adding the totals from steps (2) to step (5) which would be grater than 16.302. But how do you work out step (6)?

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Re: Combinatorics (permutation) [#permalink]

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New post 13 Oct 2008, 11:41
piper wrote:
Hi, I need help working out a type of permutation. EG I am using the 26 letters from the alphabet to create a 3 letter code where order matters. However, any letter can be repeated only twice. How many possible codes can I create?

If you need more clarity see the question below. The line in bold is where I got the question above from. If there is an easier way to ans the question below, please let me know. Thanks.

------------------------------------------------------------------

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

o 2,951
o 8,125
o 15,600
o 16,302
o 18,278

My shot at working this out.

1) There are 3 Code types A, BC, ABC
2) for A types there will be 26 codes
3) for BC types with diff letters there will be 650 codes (from permutation 26X25)
4) for BC types with same letters there will be 26 codes (eg AA, BB, CC)
5) for ABC types with diff letters there will 15600 codes (from permutation 26x25x24)
5) for ABC types with all same letters there will 26 codes (eg AAA, BBB, CCC)
6) for ABC types with 2 similar letters (eg AAB, BBA, CCB,) I am not sure how to work out


26*25*24/2*2*2 should produce the 6th step i think...
_________________

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Kudos [?]: 36 [0], given: 1

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Joined: 17 Jun 2008
Posts: 1540

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Re: Combinatorics (permutation) [#permalink]

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New post 13 Oct 2008, 12:09
Here is my approach.

Codes with a single letter = 26
Codes with two letters = 26 * 26 (since the letter can repeat)
Codes with three letters = 26* 26* 26 (since the letter can repeat)

Hence, total = 26 + 676 + 17576 = 18278

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Re: Combinatorics (permutation) [#permalink]

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New post 13 Oct 2008, 12:13
piper wrote:
Hi, I need help working out a type of permutation. EG I am using the 26 letters from the alphabet to create a 3 letter code where order matters. However, any letter can be repeated only twice. How many possible codes can I create?

If you need more clarity see the question below. The line in bold is where I got the question above from. If there is an easier way to ans the question below, please let me know. Thanks.

------------------------------------------------------------------

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

o 2,951
o 8,125
o 15,600
o 16,302
o 18,278



Since the letter can be repeat. The number of available letters will always be 26.

Case 1: one-letter code
Number of available codes = 26

Case 2: two-letter code
Number of available codes = 26 x 26

Case 3: three-letter code
Number of available codes = 26 x 26 x 26

Total codes = 26 + (26 x 26) + (26 x 26 x26)
= 18,278

The answer is E.

Kudos [?]: 42 [0], given: 0

Re: Combinatorics (permutation)   [#permalink] 13 Oct 2008, 12:13
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Combinatorics (permutation)

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