1. Permutations and Combinations
AII
Permutations and Combinations
Adapted from resources at:
and

2. What do you call this thing?
It’s a combination lock, right?

3. Permutations & Combinations
A combination is an arrangement of items in which ORDER DOES NOT MATTER.
A permutation is an arrangement of items in a particular order.
Notice, ORDER MATTERS!

4. What should we call this thing?
So it’s really a permutation lock.

5. How many ways can we arrange the letters ABC in groups of 2?
____ ____
AB AC BA BC CA CB
How could we do it if we didn’t want to
write them all out?
3 ____
How many choices are there for first blank?
3 2
For the second blank?
(3)(2) = 6
Is this a permutation or a combination?
It’s a permutation, because order matters.
(For example, BA and AB are different things.)

6. Permutations The exclamation point represents a factorial.
To find the number of Permutations of n items chosen r at a time, you can use the formula
The exclamation point represents a factorial.
n! is the product of all whole numbers less than or equal to n.
For example, 5! = (5)(4)(3)(2)(1)
0! is defined to be 1.

7. Permutations
For the ABC example, we had 3 letters, and chose 2:

8. If you wanted to do a permutation of 10 objects in groups of 7:
In the TI-83…
If you wanted to do a permutation of 10 objects in groups of 7:

9. Permutations =24,360 Practice:
A combination lock will open when the right choice of three numbers (from 1 to 30, inclusive) is selected. How many different lock combinations are possible assuming no number is repeated?
=24,360

10. Combinations
To find the number of combinations of n items chosen r at a time, you can use the formula
Or, on the calculator, you’ll find the combination choice just below the permutation choice.

11. Combinations
For example, to choose 2 letters out of 3 in ABC, we could have:
A & B A & C B & C

12. Combinations
To play a particular card game, each player is dealt five cards from a standard 52-card deck. How many different hands are possible?
Practice:
Why is this a combination, and not a permutation?
The order doesn’t matter. (Having 4 aces and a king is the
same as getting an ace, a king, then 3 aces.)

13. Permutation or Combination?
From a club of 24 members, a President, Vice President, Secretary, Treasurer and Historian are to be elected. In how many ways can the offices be filled?
permutation

14. Permutation or Combination?
A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions?
combination

15. Permutations or Combinations?
A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting line up of one center, two forwards, and two guards?
combinations
Center:
Forwards:
Guards:
Thus, the number of ways to select the starting line up is (2)(10)(6) = 120.