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A certain stock exchange designates each stock with a 1,2 or [#permalink]
19 Dec 2007, 05:09

A certain stock exchange designates each stock with a 1,2 or 3-letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

Re: permutations - DIFFICULT [#permalink]
19 Dec 2007, 13:20

marcodonzelli wrote:

A certain stock exchange designates each stock with a 1,2 or 3-letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

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

This wasn't too difficult, just may seem so b/c we don't usually encounter these types of perm problems..

Re: permutations - DIFFICULT [#permalink]
21 Dec 2007, 21:19

marcodonzelli wrote:

A certain stock exchange designates each stock with a 1,2 or 3-letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

last digit of 26: 6 last digit of 26^2: 6 last digit of 26^3: 6 last digit of the sum: 8

Therefore, E

This short cut for calculation is awesome! Thanks Walker!

Walker,
There is a gap in my knowledge of this problem. I can understand only the case 26*26*26. B/c the codes can be designate by 26C1*26C1*26C1. Can Walker make clear why I must plus 26 and 26*26?