# Permutations - Combinations

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```					            Factorial Rule

A collection of n different items can be
arranged in order n! different ways.
(This factorial rule reflects the fact that
the first item may be selected in n
different ways, the second item may be
selected in n – 1 ways, and so on.)
Combinations Rule

Requirements:
1. There are n different items available.
2. We select r of the n items (without replacement).
3. We consider rearrangements of the same items to be the
same. (The combination of ABC is the same as CBA.)

If the preceding requirements are satisfied, the number of
combinations of r items selected from n different items is

n!
nCr = (n - r )! r!
Consider the collection consisting of the
five letters a, b, c, d, e.
List all possible combinations of three
letters from this collection of 5 letters.

5 c3      10
The quality assurance engineer of a television
manufacturer inspects TVs in lots of 100. He selects 5 of
the 100 TVs at random and inspects them thoroughly.
Assuming that 6 of the 100 TVs in the current lot are
defective, find the probability that exactly 2 of the 5 TVs
selected by the engineer are defective.

100 C5  75, 287,520
6   C2  15,   94   C3  134, 044
15 134,044  2,010,660
 the probability that exactly 2 of the 5 TVs selected
2, 010, 660
are defective is:               0.027
75, 287,520

There is a 2.7% chance that exactly 2 of the
5 TVs selected by the engineer will be defective.
Find   10C2

A. 80,640
B. 40,320
C. 45
D. 5
Find   10C2

A. 80,640
B. 40,320
C. 45
D. 5
Permutations Rule
(when items are all different)
Requirements:
1. There are n different items available. (This rule does not
apply if some of the items are identical to others.)
2. We select r of the n items (without replacement).
3. We consider rearrangements of the same items to be
different sequences. (The permutation of ABC is different
from CBA and is counted separately.)
If the preceding requirements are satisfied, the number of
permutations (or sequences) of r items selected from n
available items (without replacement) is

n Pr =          n!
(n - r)!
In the NY State lottery, a player wins first prize by
selecting the correct 6-number combinations when
6 different numbers from 1 to 51 are drawn. Find the
probability of winning. (Order is irrelevant.)

51   C6  18, 009, 460
1
P(winning)=
18, 009, 460
How many ways can the letters be arranged in the
following words.
(a) MISSISSIPPI
(b) STATISTICS

11!
(a)         34, 650
4!4!2!
10!
(b)         50, 400
3!3!2!
If 10 newborn babies are randomly selected, find
probability of getting 5 boys and 5 girls in any order.

10!
2  1024
10
 252
5!5!

252
P(getting 5 boys and 5 girls in any order)=
1024

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 views: 26 posted: 9/10/2011 language: English pages: 12