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GMAT Prep problem...

by adi_800 » Sat Aug 28, 2010 3:35 am
A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 alphabets. If the letters may be replaced 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. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278

Explain!
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by sirisha.g » Sat Aug 28, 2010 3:48 am
IMO E.

My explanation goes like this

there can be a one or two alphabet or three alphabet codes=> combination of 1+2+3 alphabet codes.

1 alphabet code= 26c1

2 alphabet code: 26c1*26c1(since the alphabets are replaced. you will have 26 each time to select)

3 alphabet code: 26c1*26c1*26c1

sum=18278
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by diebeatsthegmat » Sat Aug 28, 2010 11:33 am
adi_800 wrote:A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 alphabets. If the letters may be replaced 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. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278

Explain!
we have to fine a code with one or two or three letters. supposed : A, AA, BBB
because these letters are selected from 26 alphabet and they can be replaced or they are repetitive
thus for A =26 ways
BB=26*26 ways
CCC=26*26*26 ways
thus we will have 26+26*26+26*26*26= E
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