MCA Prep – Worksheet #4
ANSWER KEY
Probability & Statistics
Advisor ____________________
Factorial … Arrangements
Definition of terms:
Factorial: The factorial of a non-negative integer n ( denoted by n! ) is the
product of all positive integers less than or equal to n. For example:
[Point of interest: The value of 0! is 1, according to the convention for an empty product.]
It is often used in permutations and combinations to find out how many arrangements are possible.
Example:
Billy is appearing in a talent show in which there are 6 acts.
How many different ways can those 6 acts be arranged in the
program if it is done randomly?
Answer: The answer is 6! = 6x5x4x3x2x1 = 720 ways.
Answer the following:
1)
Mrs. Phillips is in charge of setting up the guest speakers for the
graduation program. Besides herself, there are four other speakers.
How many different ways can she arrange the 5 of them onstage?
C) 120 ways
2)
It is Billy’s job to arrange the winning paintings on the wall to show to
the public. He has been given 7 paintings in all. How many ways can
he arrange them?
D) 5040 ways
3)
Mr. Vincent was giving 4 kids on the soccer team a ride to practice.
How many ways could he arrange them in the car?
B) 24 ways
These get a little trickier:
4)
If Mr. Burton is making out the lineup for the baseball game, how
many ways can he arrange the 9 players, if he definitely wants the
catcher to bat last?
C) 40,320 ways
5)
Mary is arranging her 5 bridesmaids regarding what order they will
stand in at the wedding. If her maid of honor must stand next to her,
how many ways can she place her other friends?
B) 24 ways
Work these problems at the end of Phase I:
6)
Sandy was given the job of arranging the guest speakers for the banquet. If 6 people are
speaking, how many different ways can she seat them on the stage?
D) 720 ways
7)
Tommy is part of a small variety presentation being given to the middle school students. If
there are 5 acts total, how many different ways can they arrange these acts in the show?
C) 120 ways
Work these problems at the end of Phase II:
8)
Tilly is hoping that when the winning portraits are hung in the hallway that hers will be first.
Since there are 6 winning portraits in all, how many different ways could they be hung?
D) 720 ways
9)
Sam and his dog, Rex, are part of a dog show. For the big finale, the 4 best dogs are being
marched out randomly and Rex is one of those dogs. How many different ways can those
dogs be brought out at the end of the show?
B) 24 ways
Work these problems at the end of Phase III:
10)
Mr. Marvin is giving 6 of the players on the track team a ride to the meet. How many
different ways can he arrange them in his van?
D) 720 ways
11)
Shay has the names of the 7 candidates written on separate sheets of paper. The order in
which they are drawn determines the duties of each candidate. How many different ways
can the names be drawn from the box?
D) 5040 ways
Work these problems just prior to the MCA Test:
12)
Sam has the duty of choosing the order in which the candidates will speak at the debate.
He has been told to have the names chosen randomly. If there are 5 candidates, how many
different ways can he arrange them as speakers?
C) 120 ways
13)
Cheryl is planning the local variety show and has only 6 acts to put in it. She wants to
randomly choose the order in which they will perform. How many different ways can she
place them in the program?
D) 720 ways
14)
The athletic department has 4 trophies to display that various teams won during the year.
In order to be impartial, he wants to arrange them in random order. How many different
ways can he display these trophies?
B) 24 ways