permutation

[albema]

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

A. 4
B. 5
C. 6
D. 7
E. 8

B

[dmateer25]

If we had 4 letters:

A
B
C
D
AB
AC
AD
BC
BD
CD

Only 10 distinct possibilities.

5 Letters
A
B
C
D
E
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE

15 Distinct Possibilities.


Another approach would be:

4 single letters + 4C2
4 + 6 = 10

Not enough

5 single letters + 5C2
5 + 10 = 15

This would be enough.

[cramya]

Since it doesnt take much time listing out the possibiltiies would be a safe approach.

I think Dmateer has explained it quite well!

[canuckclint]

It is unclear if order matters.
ie AB and BA are different.

Given order does not matter and want to do it automatically take

(x c 2) + x for a quicker solution.

[shafeek]

Hi all, this is my first post in this wonderful site that i discovered yesterday. With only 2 weeks left for my GMAT exam i am trying to cover as much as ground as possible in this site. Pray for me guys..

canuckclint order matters.. the question states that: a pair of distinct letters written in alphabetical order
so AB is correct but you cant consider BA