Expert: Josh - 5/23/2005

Question
How many ways can you choose 3 CDs from a group of 5?

Answer
Hi Andrew,

The answer depends on whether the order of appearance makes any difference. Since your question is about permutation, I guess it does matter.

The answer is given by P(N,k)=N!/(N-k)!, where N=5, the number of CDs to choose from; k=3, the number of times you select a CD (without replacement after each selection).

The notation N! is called "N factorial". It is defined by the product of integer numbers, starting from N, then, N-1, N-2 and so forth, all the way down to 1.

i.e., N! = N*(N-1)*(N-2)*...*1.
Similarly, (N-k)! = (N-k)*(N-k-1)*(N-k-2)*(N-k-3)*...*2*1.

Just out of interest, 0! is defined as 1.

e.g., When N=5, N!=5*4*3*2*1=120, (N-k)!=(5-3)!=2!=2*1=2.
So, the answer is N!/(N-k)!=60 ways to choose 3 from 5.

A,B,C; A,C,B
A,B,D; A,D,B
A,B,E; A,E,B
A,C,D; A,D,C
A,C,E; A,E,C
A,D,E; A,E,D

B,A,C; B,C,A
B,A,D; B,D,A
B,A,E; B,E,A
B,C,D; B,D,C
B,C,E; B,E,C
B,D,E; B,E,D

C,A,B; C,B,A
C,A,D; C,D,A
C,A,E; C,E,A
C,B,D; C,D,B
C,B,E; C,E,B
C,D,E; C,E,D

You can easily work out the other 24 combinations which i have left out.

Cheers