Combination

[JeetGulia]

A certain stock exchange designates each stock with one, two or three letter codes, where each letter is selected from the 26 letters. If the letters may be repeated and if the same letters used in a different order is a different code, how many different stocks codes are possibile.

a) 2,951
b) 8125
c) 15,600
d) 16,302
e) 18,278

ans E

Please help

[Rahul@gurome]

One letter code can be designated in 26 ways.
Two letter codes can be designated in 26^2 ways.
Three letter codes can be designated in 26^3 ways.
Therefore, number of stock codes possible = 26 + 26^2 + 26^3 = 18,278

The correct answer is [spoiler](E)[/spoiler].

[rb90]

But why dont we have to use permutation also in this sum? Since the sum hints at arrangement ..please help,im confused.

[euro]

But why dont we have to use permutation also in this sum? Since the sum hints at arrangement ..please help,im confused.

We don't use permutation {nPr formula} because no restriction is imposed here...
"the letters may be repeated and if the same letters used in a different order is a different code"

In case of two letter codes, the first position can be filled by any of the 26 alphabets and the second position can also be filled by any of the 26 alphabets. The two positions can be filled in 26 x 26 = 26^2 ways.

Similarly, for three-letter codes, the three positions can be filled in 26^3 ways (since repetition is allowed).

If repetition is allowed, for 'n' distinct objects taken 'r' at a time, the number of arrangements possible is n^r.

[msbinu]

But why dont we have to use permutation also in this sum? Since the sum hints at arrangement ..please help,im confused.

Hi ,
We can use permutation also to solve this.

1 letter code can be selected from 26 letters using 26P1 ways = 26!/25! = 26
2 letter code could be selected in 26P1 * 26 P 1 ways = 26 * 26 = 676
3 letter code could be selected in 26p1 * 26P1 * 26 P1 ways = 26 * 26 * 26 = 17576

Hence total = 18278 .

Hope this helps