The document discusses permutations and combinations. It provides examples of calculating permutations, such as the number of ways 3 horses could finish in different positions in a race of 8 horses. It also gives examples of calculating the number of possible combinations for different scenarios, such as the number of possible 3-digit combinations for a locker combination lock with 35 or 60 possible numbers.

1. Permutations or
quot;Why this isn't really
a combination lock.quot;
Project365 - 290 by flickr user MikeNeilson

2. (a) How many numbers of 5 different
digits each can be formed from the
digits 0, 1, 2, 3, 4, 5, 6?

3. (a) How many numbers of 5 different
digits each can be formed from the
digits 0, 1, 2, 3, 4, 5, 6?
(b) How many of these numbers are even?

4. (a) How many numbers of 5 different
digits each can be formed from the
digits 0, 1, 2, 3, 4, 5, 6?
(c) How many of these numbers are divisable
by 5?

5. Permutations
Permutation: An ordered arrangement of objects without
repetition.
A.K
.A t
he
quot;Pic
kquot; f
orm
Formula:
ula.
n is the number of objects to pick from
r is the number of objects to be arranged
is read as quot;n pick rquot;
means: Given a set of n objects, how many ordered
arrangements can be made using only r of them at a time?

6. Example: There are 8 horses in a race. In how many ways can three
of them finish first, second and third?
Solution by the Fundamental Solution as a Permutation
Principle of Counting
8 • 7 • 6 = 336
1st 2nd 3rd

7. The lock on my locker has 35 different numbers on it.
How many different 3-digit quot;keysquot; exist to unlock it?
On the calculator:
[MATH] [<] [2]
What if it had 60 different numbers on it?

8. How many different urls can tinyurl.com possibly make:
if it is NOT case sensitive?
if it IS case sensitive?