1.Bugs Bunny, Porky Pig, Tweety Bird, and
Daffy Duck are going to the movies (they
are best friends). How many different ways
can they sit in seats A, B, C, and D below?
A
B
C
D
24
2. Coach Elkins is picking a captain and cocaptain from his 15 players. How many
possibilities does he have if they are all
equally likely?
210
GPS Algebra
UNIT QUESTION: How do you use
probability to make plans and predict
for the future?
Standard: MM1D1-3
Today’s Question:
What is the difference between a
permutation and combination?
Standard: MM1D1.b.
Combinations
• A selection of objects in which order
is not important.
• Example – 8 people pair up to do an
assignment. How many different
pairs are there?
Combinations
AB AC AD AE AF AG AH
BA BC
BD BE BF
BG BH
CA CB
CD CE
CG CH
CF
DA DB DC DE DF DG DH
EA EB EC
ED EF
EG EH
FA FB
FD FE
FG FH
FC
GA GB GC GD GE GF GH
HA HB HC HD HE HF HG
Combinations
• The number of r-combinations of a
set with n elements,
• where n is a positive integer and
• r is an integer with 0 <= r <= n,
• i.e. the number of combinations of r
objects from n unlike objects is
n!
n Cr 
r !  n  r !
Example 1
• How many different ways are there
to select two class representatives
from a class of 20 students?
Solution
• The answer is given by the number of
2-combinations of a set with 20
elements.
• The number of such combinations is
20!
 190
20 C2 
2!18!
Example 2
From a class of 24, the teacher is
randomly selecting 3 to help her with a
project. How many combinations are
possible?
24!
 2024
24 C3 
3! 21!
Your turn!
For your school pictures, you can
choose 4 backgrounds from a list of 10.
How many combinations of backdrops
are possible?
10!
 210
10 C4 
4! 6!
Your turn!
Venus Williams randomly selects 3 people
out of her class of 20 to go to the courts
and help her get ready for a tennis match.
How many possibilities of people does she
have?
20!
 1140
20 C3 
17! 3!
Clarification on Combinations and
Permutations
• "My fruit salad is a combination of apples,
grapes and bananas"
We don't care what order the fruits are in,
they could also be "bananas, grapes and
apples" or "grapes, apples and bananas", its
the same fruit salad.
Clarification on Combinations and
Permutations
• "The combination to the safe is 472".
Now we do care about the order. "724"
would not work, nor would "247". It has to
be exactly 4-7-2.
To sum it up…
• If the order doesn't matter, then it is a
Combination.
• If the order does matter, then it is a
Permutation.
A Permutation is an ordered Combination.
How many
ways???