There are 120 possible phone numbers that meet the given conditions: - The first two digits are 36 - The third digit is even - The fourth digit is greater than 5 - The fifth and seventh digits are odd - The sixth digit is 2

1. How many phone numbers can be made under the following conditions:
(First digit cannot be 0 or 1 because you'll get the operator or long distance.)
• The first two digits are 3 followed by 6
• The third digit is even
• The fourth digit is greater than 5
• The fifth and seventh digits are odd
• The sixth digit is 2

2. Permutation: An ordered arrangement of objects without repetition.
Formula: A.K.A the "Pick" formula.
n is the number of objects to pick from
r is the number of objects to be arranged
is read as "n pick r"
means: Given a set of n objects, how many ordered
arrangements can be made using only r of them at a time?
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

3. How many ways can the batting order of a 9-member softball team be listed?

4. A 120-room hotel has reservations from 6 guests for 6 different rooms. In how
many ways can the rooms be assigned?

6. Permutations of Non-Distinguishable Objects
The number of ways to arrange n objects that contain
sets of non-distinguishable objects is given by:
Example: How many different "words" can be made form the letters in
the word: (a) BOOK (b) MISSISSIPPI
# of I's = 4
# of O's = 2 ∴
# of S's = 4
# of P's = 2 ∴