1. Permutations* (arrangements) and Combinations* (groups)
*Without replacement
Copyright © 2003, N. Ahbel

2. A B D C A B A C A D B A B C B D C A C B C D D A D B D C
How many arrangements of 4 items can be made taken 2 at a time? A B
How many groups of 4 items can be made taken 2 at a time? A C
same group A D B A B C
When order is important use permutations. B D
When order isn't important use combinations. C A C B C D D A D B D C

3. A B D C A B A C A D B A B C B D C A C B C D D A D B D C
How many arrangements of 4 items can be made taken 2 at a time? A B
How many groups of 4 items can be made taken 2 at a time? A C
same group A D B A B C
When order is important use permutations. B D
When order isn't important use combinations. C A C B C D D A D B D C

4. For this problem:

5. In General:
and
substituting
we get or

6. To write nPr, start expanding n!, but stop after r factors.
Permutations can be computed by formula or by thinking of factors.
nPr is similar to n!.
To write nPr, start expanding n!, but stop after r factors.
To write 6P2 expand 6!, but stop after 2 factors.
2 factors
Another example

7. Permutations* (arrangements) and Combinations* (groups)
*Without replacement
Copyright © 2003, N. Ahbel