Math 30-2
Permutations & Combinations: Lesson #4
Permutations with Repetitions
Objective: By the end of this lesson, you should be able to:
- determine the number of permutations where some elements are identical
- explain why there are fewer permutations when some elements are identical
Warm-Up
 How many permutations are there of the letters in the words FUEL?

List all the permutations of the letters in the word FULL. How many are there?

Why does FULL have fewer permutations than FUEL?

List all the permutations of the letters in the word LULL. How many are there?
There are ___________ permutations of a set of objects when some of the objects are identical,
since a new arrangement is not formed when the identical objects are interchanged.
The number of permutations of n objects if there are a alike of one kind, b alike of another kind,
and c alike of yet another kind, is
e.g. 1) Determine the number of permutations of the letters in the word:
a) BUBBLE
b) PARALLEL
c) MISSISSIPPI
Math 30-2
Permutations & Combinations: Lesson #4
e.g. 2) A lacrosse team’s record over a season was 15 wins, 4 losses, and 2 ties. In how many
orders could this record have occurred?
e.g. 3) Sarah wants to visit Tamina. The two girls’ houses are shown on the grid below. The
lines represent roads. If Sarah stays on the roads and always moves closer to Tamina’s
house, how many different paths could she take?
Sarah’s house


Tamina’s house
e.g. 4) An airline pilot reported his itinerary for 7 days. He spent 1 day in Winnipeg, 1 day in
Regina, 2 days in Edmonton, and 3 days in Yellowknife. How many different itineraries
are possible if he started and ended in Yellowknife?
e.g. 5) How many distinct arrangements of the letters in the word POPPIES can be made if:
a) there are no restrictions?
b) the first letter is P?
c) all of the P’s are together?
Assignment:
p. 104-107 #2, 4-7, 9-10, 12, 15-18