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Geometry & Finite H
Mr. Russo
Name: _______________________
Date: _______________________
Factorials & Permutations
Factorial: The product of a whole number and every whole number smaller than it, except zero. Denoted with
an exclamation point, “!”.
Let’s pretend there are 5 seats and 5 people. How many different ways can they be seated?
___  ___  ___  ___  ___ = _____ = _____
You can also use MATH, PRB, #4 on the calculator.
Permutation: An arrangement of objects in a specific order.
What if there were only 3 seats in which to sit, but still 5 people?
___  ___  ___ =
This number, ______, is the “number of permutations of 5 things, taken 3 at a time.” We write this 5 P3 .
There is a formula for permutations:
n
Pr 
n!
(n  r )!
(n is the number of things you’re choosing from,
r is the number of spots you’re putting them in.)
Check that it works when n = 5 and r = 3…
You can also do these on the graphing calculator: MATH, PRB, #2.
Try these chumpies!
1.) Evaluate 6 P2 .
2.) Evaluate
10
P4 .
3.) Evaluate 4 P4 . Do you recognize this number? (Use the formula. You may find this useful: 0! = 1)
4.) Write as a permutation, then solve: A teacher wants to write an ordered 5-question quiz from a pool of 8
questions. How many different forms of the quiz can the teacher write?
5.) Write as a permutation, then solve: The Hawaiian alphabet has only 13 letters. How many “words”
(permutations) could be made using 4 different letters?
(Hopefully you got 30, 5040, 24 [it’s 4!], 8 P5  6720 ,
13
P4  17,160 )
Not every “counting” problem uses the permutation formula. You have to figure out what the best method is to
solve each problem.
6.)
7.)
8.) For this problem, assume the number CAN start with 0.
Answers:
6.) 362,880; 60,480; 2880; 2880; 14,400
7.) 720, 30, 240
8.) 16,807; 2520; 9603
HW 4
1.) Four students are to be chosen from a group of 10 to fill the positions of president, vice-president, treasurer
and secretary. In how many ways can this be accomplished? Write this as a permutation 1st.
2.) How many ways can the letters MATH be arranged?
3.) A lock contains 3 dials, each with ten digits. Assuming a digit could be repeated, how many possible
sequences of numbers exist?
4.) A shelf can hold 7 trophies. How many ways can the trophies be arranged if there are 12 trophies available?
5.) Bill has 3 pairs of pants, 5 shirts and 2 pairs of shoes. How many outfits can he make?
6.)
7.)
8.) Evaluate each of the following. Show all work!
a. 7 P2
b. 12 P1
d. P(9, 0)
e.
P(11, 4)
4!
9.) Solve for n. Show all work!
a. P(n, 2) = 20
10.)
b. P(n, 2) = 12
c. 8 P8
f.
P(10, 6)
6!