Page 174 - Math Course 1 (Book 2)

Permutations and Combinations

Use a Combination Real World Example

Example TENNIS
The players listed are playing singles in a tennis
tournament. If each player plays every other player
once, what is the probability that Kyle plays in the
HATS f rst match?
How many ways can a window dresser choose two
hats out of a fedora, a bowler, and a sombrero? Thomas Carl
Ager Jack
Since order is not important, this arrangement is a
combination. Brian Seth
Kyle Pedro
First, list all of the permutations of the types of
hats taken two at a time. Explore The order in which the players are
selected is not important, so this is a
Then cross off arrangements that are the same as combination.
another one.
Plan Find the combination of 8 people taken
FB and BF are
FB and BF are not
not different in 2 at a time. This will give you the
different in this
this case, so number of matches that take place
cross off one of
FB FS BF BS SF SB case, so cross off during the tournament. Then f nd how
them.
one of them.
many of the matches involve Kyle.
There are only three different arrangements.
8 • 7
Solve C(8, 2) = = 28 there are 28 ways to
There are three ways to choose 2 • 1
Answer two hats from three possible choose 2 people. Kyle plays each person
hats. once during the tournament. If there
are 7 other players, Kyle is involved in
PENS 7 matches. So the probability that Kyle
1
7
How many ways can a customer choose two pens plays in the f rst match is or .
from a purple, orange, green, red, or black pen? 28 4
The arrangement is a combination because order Check List all the 2-player matches in the
is not important. tournament. Check to see that there
are 28 matches.
First, list all of the permutations.

Then cross off the arrangements that are the Answer 7 or 1
same. 28 4

PO PG PR PB OP OG OR
OB GP GO GR GB RP RO
RG RB BP BO BG BR

There are 10 ways to choose
Answer two pens from f ve possible
colored pens.

166