# Dinner Party___ by ewghwehws

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```									Dinner Party!!!

By Becky Rose
7th Grade Math Teacher
Western Peaks Elementary School
Dysart Unified School District
Materials Needed:
• 2 color counters (10 for each small
group)
• 1 dry erase marker for each group
• pencil to record answers
• paper to write out questions
Directions:
• Put your class into groups of 2-3
students each.
• Distribute materials to each group.
• Have students label the 2 color
counters using the dry erase marker.
Labels should be as follows:
yellow – seats A-E
red – 5 different guests names
(student selected)
Dinner Party Dilemma…
Imagine that you have five dinner
guests coming over for a dinner
party. While you are thinking about
seating arrangements, you realize
that there are many different ways
you could seat your guests. But is
there a way to figure out exactly how
many arrangements are possible?
Remember, people are “available”
until they are assigned a seat.
What to do…
• Use the labeled color counters and
follow the directions for each step.
• Record your results after each
question.
• Remember, people are “available”
until they are assigned a seat.
• Once a person has been assigned a
seat, they can no longer be
“available” for any other seat around
the table.
Pick a person to sit in seats A, B, C, D, and E one at a time
and in order. Answer the following questions one at a time as
you fill in the number and name you have picked for each seat.

1.   How many people are available      to sit in seat A?
___________________
2.   How many people are available      to sit in seat B?
___________________
3.   How many people are available      to sit in seat C?
___________________
4.   How many people are available      to sit in seat D?
___________________
5.   How many people are available      to sit in seat E?
___________________
Write the mathematical
expression…
In questions 1-5 you counted the
number of persons available to fill
each seat.
How could you figure out the total
number of ways there are to fill all of
the seats?
Write this out as a mathematical
expression.
Extension Activity
• Using the mathematical expression
you wrote, answer the following:
How many ways is it possible to
arrange 5 people in 5 seats?
6 people in 6 seats?
7 people in 7 seats?
Key Terms
• Permutations: a category of
probability in which a series of things
can be put in order
• Factorial: the product of all positive
integers less than or equal to a given
positive integer
• Probability: the likelihood of an
event to occur; the odds of
something happening
Solutions:
• 1: 5
• 2: 4
• 3: 3
• 4: 2
• 5: 1
• Expression:    5 * 4 * 3 * 2 * 1 or 5!
This could also be written out as follows:
n * (n-1) * (n-2) * (n-3) * 1
when n = total number of options available
• Extension:     5!    =      120
6!    =      720
7!    =      5040

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