Section 10.5 and 10.6
Combinations
Activity #1
• See the problems on your sheet.
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!
Remember this problem?
• 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”
Remember this problem?
• How is it different if we…
• Elect two representatives to serve on the
University Senate
• What if we elected three representatives?
Combinations
• If you are choosing m out of n items where
the order they are picked DOES NOT
MATTER, you are calculating
combinations.
• C(n,m) = n!
(n-m)! m!
Combinations
Since:
• P(n,m) = n!
(n-m)!
• C(n,m) = n!
(n-m)! m!
=
P(n,m)
m!
Activity #2
• Calculate the value of:
1. C(7,3)
2. C(10,5)
3. C(6,5)
4. C(6,6)
5. C(n,3)
6. C(n,n-3)
Activity #3
• See the problems on your sheet.