Combinations 11'3

1
Combinations 11.3
a) The items are selected from the same group b)
No item is used more than once. c) The order of
items make NO difference, different than
permutations
2
Combinations are mathematically related to
permutations.
n C r
3
An election ballot asks voters to select three
city commissioners from a group of six
candidates. In how many ways can this be done?
6 C 3
20
4
Solve the n C r expressions.
12 C 5
792
5 C 0
1
8
5
Of 12 possible books, you plan to take 4 with you
on vacation. How many different collections of 4
books can you take?
n C r
12 C 4
495
6
Of the 100 people in the U. S. Senate, 18 serve
on the foreign Relations Committee. How many
ways are there to select Senate members for this
committee (assuming party affiliation is not a
factor in selection)?
n C r
100 C 18
3.07 x 10 19
7
Does the problem involve a Permutation or
Combination
In a race in which six automobiles are entered
and there are no ties, in how can the first three
finishers come in?
6 P 3
120
8
Does the problem involve a Permutation or
Combination
From a club of 20 people, in how many ways can a
group of three members be selected to attend a
conference ?
1140
20 C 3
9
Does the problem involve a Permutation or
Combination
To win Lotto a person must correctly select 6
numbers from a collection of 54 numbers. How
many different selections are possible ?
54 C 6
25,827,165
10
Does the problem involve a Permutation or
Combination
Using 31 ice cream flavors, how many three scoop
ice cream cones, with different flavors for each
scoop, can you create if it is important to you
which flavor goes on top, middle, and bottom ?
31 P 3
26,970
11
Does the problem involve a Permutation
or Combination
In how many ways can a committee of four men and
five women be formed from a group of seven men
and seven women?
7 C 4
X
7 C 5
735
12
Does the problem involve a Permutation or
Combination
How many different four-letter passwords can be
formed from the letters A,B,C,D,E,F, and G if no
repetition of letters is allowed ?
7 P 4
840
13
Does the problem involve a Permutation or
Combination
How many different committees can be formed from
5 professors and 15 students if each committee is
made up of 2 professors and 10 students?
5 C 2
X
15 C 10
30030
14
Homework

• Pg 578
• 3-39 multiples of 3