May 22, 2013
9.1 Combinations
the number of ways to SELECT r objects, regardless of
the order in which we arrange them.
How many ways can you select 3 objects from a set of 4?
A
B
C
D
May 22, 2013
Combination Counting Formula:
The number of combinations of n objects taken r at a
time is denoted:
C
n r
=
n!
r!(n-r)!
Proof: Every permutation can be thought of as an unordered
selection of r objects followed by a particular ordering of
the objects selected.
P =
n r
C r!
n r
May 22, 2013
Every NBA basketball team has 12 players. How many different
starting 5's are possible?
May 22, 2013
May 22, 2013
In the game of bridge, each player is dealt a 13-card hand
from a standard deck of 52 cards. How many different
card hands are possible?
May 22, 2013
A lottery requires winners to pick 6 integers between 1 and 45.
How many different lottery tickets are possible?
May 22, 2013
A pizzeria offers any combination of up to 8
different toppings. How many different pizzas
can be ordered if:
a. we choose any 3 toppings?
b. we choose any number of toppings (0 - 8)?
May 22, 2013
Formula for Counting Subsets of an n-set:
There are 2n subsets of a set with n objects (including
the empty set and the entire set).