Section 6.3 Notes Multiplication Principle

Section 6.3 Notes
Multiplication Principle
Suppose we toss a coin twice. How many outcomes are possible?
If we toss a coin and roll a six-sided die, how many outcomes are possible?
Multiplication Principle: Suppose there are k tasks, and that the first
can be done in N1 different ways, the second can be done in N2 different ways,
. . ., the k’th can be done in Nk different ways. Then the total number of ways
the different tasks can be performed is
N1 ∗ N2 ∗ . . . ∗ Nk .
Example: If Ashlee has 12 shirts, 5 pairs of pants, and 7 pairs of shoes,
how many different outfits can she make?
Example: If a computer user’s password must consist of 6 lower-case consonants, how many different possibilities are there if
(a.) repetitions are allowed?
(b.) no repetitions are allowed?
Example: How many different 7-digit phone numbers are there, if the first
digit can’t be zero?
Example: Andrew can’t remember his computer password. However, he
remembers the following information:
• it is either 7 or 8 letters long
• it is case-sensitive
• it begins with an upper-case letter
• it ends with a number
• the 5th character is a “b”
How many different passwords will he have to try?