GMATFocus: Why permutation and not combination ?

[sudipto]

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A) 5 to 4
B) 3 to 2
C) 2 to 1
D) 5 to 1
E) 6 to 1

The OA says that its the ratio of 10P5 to 10P4 . I thought that we wererequired to "choose" and not "arrange" in this problem so combination (choosing) seems reasonable no ?

BTW, OA is E

[cramya]

Think of it this way.

Lets take just AB. Is code AB same as code BA? The answer is no.

For example lets say one password is abc and the other is bca(even though we have used the same letters the passwords are different, correct).

These are 2 different passwords and the same applies to codes above. Hence order matters PERMUTATION

[sudipto]

Thanks cramya !

I agree that the order does matter - but on the first look it does seem like a combination problem - bacause i read somewhere that " Combination is selection and permutation is arrangement" and here we are selecting 5 from 10 followed by rearranging them - so it seems like combination followed by permutation right ?

[stop@800]

[/b]sequence of different letter[/b]

means its an arrangement.