Section 10.3 and 10.4
Permutations
Activity #1
• See the problems on your sheet.
Counting with Functions
• How many different functions are available
from a set of 8 elements to a set of 5
elements?
• How many different functions are available
from a set of m elements to a set of n
elements?
Counting with Functions
• How many different one-to-one functions
are available from a set of 5 elements to a
set of 8 elements?
• How many different one-to-one functions
are available from a set of m elements to a
set of n elements?
Permutations
• If you are choosing m out of n items where
the order they are picked matters, you are
calculating permutations.
• P(n,m) = n!
(n-m)!
Permutations
Notice that:
n!
(n-m)!
= n • (n-1) • (n-2) •… • (n-m+1) • (n-m) • (n-m-1) • (n-m-2) •… • 2 • 1
(n-m) • (n-m-1) • (n-m-2) •… • 2 • 1
Which is the same as:
n!
(n-m)!
= n • (n-1) • (n-2) •… • (n-m+1)
Which may be significantly easier to calculate!
Activity #2
• Calculate the value of:
1. P(7,3)
2. P(10,5)
3. P(6,5)
4. P(6,6)
5. P(n,3)
6. P(n,n-3)
Activity #3
• We are going to elect a “student council”
from the members of today’s class.
• In how many ways can we pick a President,
Vice President, and Secretary?
• In how many ways can we do this PLUS
pick a Treasurer and “Sergeant at Arms”