Notes 14.4 - Perms and Combos.notebook

Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Bellwork
Theo's history test has 6 multiple choice questions with choices a, b, c, d, and e. If he guesses on each question, what is the probability he will get 100% on the test?
Quote of the Week: "It is hard to fail, but it is worse never to have tried to succeed."
­Theodore Roosevelt
Notes 14.4 ­ Perms and Combos.notebook
W
o
r
k
s
h
e
e
t 1
4
.3
1. 1/7
13. 1/100 or 1%
2. 2/7
14. 4/100 4%
3. 4/7
15. 36%
4. 1/4
16. 11%
5. 5/12
6. 1
7. (144 ­ 36π)/144
8. 1/4
9. 2.25π/509.22 or .004π
or 1%
10. Once
11. 9π/509.22 or 4%
12. 1/2
April 16, 2013
Notes 14.4 ­ Perms and Combos.notebook
Notes 14.4 ­ Permutations and Combinations
Permutation ­ choosing part of a set when order matters !!! *Permutations can be solved using the counting principle*
Example 1 ­ Out of 5 runners, in how many ways can
1st, 2nd, and 3rd place be awarded?
Example 2 ­ You have 7 books to place on a bookshelf.
In how many different ways can the books be arranged?
April 16, 2013
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Factorial ­ ! signifies the consecutive multiplication of a number
4! = _________________
Fancy Permutation Formula
n!
n Pr = (n­r)!
n = # of total objects (big one)
r = # of objects chosen (small one)
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Example 3 ­ Use the nPr formula: Out of 5 runners, in
how many ways can 1st, 2nd, and 3rd place
be awarded?
Notes 14.4 ­ Perms and Combos.notebook
Example 4 ­ How many different ways can 8 books be
placed on a shelf with 6 spaces?
April 16, 2013
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Combination ­ choosing part of a setwithout regard to order
Example 5 ­ List the combinations of {A, B, C, D} taken 3 at a time.
How many total combinations are there? A letter can
be used only once in a set.
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Example 6 ­ List all the combinations of 2 numbers from the set {1, 2, 3, 4}. A number can only be used once in a set. Notes 14.4 ­ Perms and Combos.notebook
Combination Formula
n!
n Cr = r!(n ­ r)!
April 16, 2013
n = # of total objects
r = # of objects chosen
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Example 7 ­ In how many ways can 3 identical jobs be
filled by a selection of 12 different people?
n!
n Cr = r!(n ­ r)!
Example 8 ­ 15 singers are trying out for Concert Choir. If
only 5 singers can make it, how many different
combinations of Concert Choir exist?
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
Example 9 ­ From 7 guys and 4 girls, how many committees
can be selected if you want 3 guys and 2 girls?
Steps to Solve:
1. Find combo for guys
2. Find combo for girls
3. Multiply results
Notes 14.4 ­ Perms and Combos.notebook
Example 10 ­ From 11 dogs and 8 cats, how many groups
can be created if you want 5 dogs and 3 cats?
April 16, 2013
Notes 14.4 ­ Perms and Combos.notebook
April 16, 2013
The tough stuff...
Determine whether the following are combinations or permutations.
1. Selecting a committee of 3 people out of a group of 20.
2. Choosing winning lottery numbers.
3. Creating a seating chart for 6 people.
4. Picking 3 letters and 3 numbers for a license plate.
5. Creating a team of 6 out of 35 people.