A certain stock exchange designates each stock with a one-,

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A certain stock exchange designates each stock with a one-, [#permalink]

30 May 2008, 06:19

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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?

A) 2951
B) 8125
C) 15600
D) 16302
E) 18278

Answer is E, please explain

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Re: Combinatorics PS [#permalink]

30 May 2008, 08:12

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Remember that Numbers can be repeated.

Number of 1 Digit Codes = 26
Number of 2 Digit Codes = 26 * 26 = 676
Number of 2 Digit Codes = 26 * 26 * 26 = 17576

Total = 26 + 676 + 17576 = 18278

In future do not put OA with the question. As people might solve it back wards to reach the solution.

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Re: Combinatorics PS [#permalink]

30 May 2008, 08:13

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You have 3 different sets of Permutations available.

First set is of stocks that have only 1 letter, or 26 possibilities

Second set is of stocks with 2 letters, or 26 * 26 possibilities

Third set is of stocks with 3 letters, or 26 * 26 * 26 possibilities.

This equal 26 +676 + 17576 = 18,278.

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Re: Combinatorics PS [#permalink]

30 May 2008, 08:42

abhijit_sen wrote:

In future do not put OA with the question. As people might solve it back wards to reach the solution.

I think the moderator/owner of the forum should add a "spoiler" function on the forum. That function is the perfect fit for this type of forum, but this forum does not have it.

Re: Combinatorics PS [#permalink] 30 May 2008, 08:42

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A certain stock exchange designates each stock with a one-,

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A certain stock exchange designates each stock with a one-,

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