Permutations and Combinations
Objectives:
…to determine and show the number of permutations and/or combinations
for an event
Assessment Anchor:
8.E.3.2 – Determine the number of combinations and/or permutations for
an event.
Vocabulary alert!!
PERMUTATION – an arrangement in which order is
important
COMBINATION – an arrangement in which order is not
important
EXAMPLES of PERMUTATIONS
1)
John, Dave, and Alex race each other. How many different ways could they
finish?
***Because order is important here…this is a permutation. We can find out how many
possibilities there are by running a calculation or by making a chart and counting.
Calculation
Chart
1st place 2nd place 3rd place
3 choices 2 choices 1 choice
3
•
2
•
6 different ways
1
Other chart
John/Dave/Alex
John/Alex/Dave
Dave/John/Alex
Dave/Alex/John
Alex/John/Dave
Alex/Dave/John
6 different ways
Permutations and Combinations
2)
Julie has 4 colored pencils. One is red, one is blue, one is green, and one is
yellow. How many different arrangements could she make on her desk?
***Because order is important here…this is a permutation. We can find out how many
possibilities there are by running a calculation or by making a chart and counting.
Calculation
Chart
1st spot 2nd spot 3rd spot 4th spot
4 choices 3 choices 2 choices 1 choice
4
•
3
•
2
•
1
24 different ways
3)
Sheila is given 5 songs to review. She is allowed to pick 3 to use during her
cheerleading team’s routine. How many permutations of 3 songs could
Sheila come up with?
Calculation
1st song
2nd song
Chart
3rd song
“Consider that sometimes, even though order would remain
important, you might be able to replicate choices…
making charts (no matter which case we’re talking
about) can eventually get awfully confusing!”
Permutations and Combinations
EXAMPLES of COMBINATIONS
4)
Kendra must choose two states to write a report on. She can choose from
Alaska, Delaware, Georgia, Pennsylvania, and Virginia. How many
different combinations of states could she pick?
***For the moment…let’s make a chart like we usually would. Then let’s see which ones are
really the same as others in the list…
A, D
A, G
A, P
A, V
D, A
D, G
D, P
D, V
G, A
G, D
G, P
G, V
P, A
P, D
P, G
P, V
V, A
V, D
V, G
V, P
Because the order in which the states are selected doesn’t really matter, this
situation is a combination. How many different combinations are there? _______
5)
The Blue Division contains 4 teams (Exeter, Reading, Mifflin, and Wilson).
Each team plays the other teams twice. How many Blue Division games are
there?
6)
Dooley has 6 colors to choose from (blue, red, green, yellow, purple, and
orange). He may use any 3 to create his picture. How many different
combinations of colors could he have?
“First determine if order is important! Then make a
chart, or perform the calculation (for permutations) to
find out how many possibilities there are.
Abbreviate things to save time!”