And/Or Permutations and Combinations
Example 1
A company makes gloves that are black, blue, burgundy or grey. Each of the colours comes in
small. medium and large size. How many different types of gloves does the company make?
Example 2
A restaurant has 4
PASCALS TRIANGLE
Version 1 of Pascals Triangle. The t0,0 stand for the term in row 0 position 0. t5,3 would stand
for row 5 position 3. Notice that the number of terms in any row is one more than the row
number. Also notice how the terms in each row are o
Permutations with Some Alike
Example 1
Determine the number of permutations of CCD. List them all.
Example 2
Determine the number of permutations of ABBAB.
Example 3
How many distinct permutations of the word Mississauga are there?
Example 4
a) How many d
Pascals Triangle Worksheet
n
1. What other expression in the form are equal to the following?
r
9
a)
2
13
b)
5
46
c)
39
26
d)
26
n
2. What other expression in the form are equal to the following?
r
8 8
a) +
3 4
17 17
b) +
6 7
28 28
And,Or Permutations and Combinations Worksheet
1. In how many ways can you roll either a sum of 9 or a sum of 12 with the following pair
of dice? The first die is 5 sided labelled 3,4,5,6,7 and the second die is 7 sided
labelled 3,4,5,6,7,8,9.
2. In how m
Permutations with Some Alike Worksheet
1. How many permutations are there of all the letters in each name:
a) Inverary
d) Penetanguishene
b) Beamsville
e) Corrolary
c) Mattawa
f) Isosceles
2. How many different five digit numbers can be formed using 3 two
Problem Solving with Pascals Triangle
Example 1
How many different paths spell HAMBURGER?
H
A
M
B
A
M
B
U
M
B
U
R
B
U
R
G
E
R
Solution
E
R
R
Example 2
How many paths will move the checker to the other side of the checker board? (Remember
that you may move
Simple Permutations and Simple Combinations
Type 1
Order Matters and You use all the objects.
A permutation of n distinct objects is_
_.
Denoted
Total number of permutations =
*read as _*
Type 2
Order Matters and You use some of the objects
A permutation
Problem Solving with Permutations and Combinations Worksheet
1.
How many different sums of money can you make with a penny, a dime, a loonie and a toonie?(zero is
not a sum)
2. How many different sums of money can be made from one $5 bill, two $10 bills a
Problem Solving with Pascals Triangle Worksheet
1. Fill in the missing numbers for this version of Pascals triangle.
_
_
_
3003
495
_
_
825
2112
_
2. Determine the number of paths that will spell the word.
P
A
T
T
E
T
R
S
T
E
N
A
T
E
R
N
S
T
T
E
R
N
S
E
R
Problem Solving with Permutations and Combinations
Example 1
We can purchase from 3 shirts, 4 shorts, 2 shoes and 6 socks. How many different
purchases can you make (not buying anything counts as a purchase)?
Example 2
Matt wishes to throw his money in to
Simple Permutations and Combinations Worksheet
1.
How many ways can you arrange the letters of the word FACTOR?
2. How many ways can you choose two jellybeans from a bag of 15?
3. How many ways can five different textbooks be arranged on a shelf?
4. How m