Combinatorics problem from GMATPREP

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abhi75: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Oct 16, 2007 5:57 am; Thanked: 3 times

Combinatorics problem from GMATPREP

by abhi75 » Mon Dec 10, 2007 8:07 pm

A certain stock exchange designates each stock with one, two or three letter code, where each letter is selected from 26 letters of the alphabet. If the letters maybe repeated and if the same letters used in different order constitute different code, how many different stocks is it possible to uniquely designate with these code.
a) 2951
b) 8125
c) 15600
d) 16302
e) 18278

I was not able to solve. Can someone please help. I will post OA soon.

Thanks.

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sujaysolanki: Master | Next Rank: 500 Posts; Posts: 214; Joined: Wed Nov 14, 2007 6:30 am; Thanked: 15 times

by sujaysolanki » Mon Dec 10, 2007 9:29 pm

one letter code: 26 = 26 codes
two letter code 26 x 26 = 676 codes
three letter code 26 x 26 x 26 = 17576 codes
total number of codes = 26 + 676 + 17576 = 18278...

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abhi75: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue Oct 16, 2007 5:57 am; Thanked: 3 times

by abhi75 » Tue Dec 11, 2007 6:33 am

Thanks for solving it. The correct OA is E.

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