PERMUTATION
AND
COMBINATIONS
BY: ELLO ESLI
RYAN
PROJECT'S OVERVIEW
• Understanding Permutation of 'n' distinct objects in a
line
• Permutations of 'k' objects from 'n' distinct objects
• Allowing constraints on permutations
• Solution to 3 past questions
• Summary of formulas and index
2
PERMUTATION OF 'n'
DISTINCT OBJECTS IN
A LINE
A permutation refers to the number of NB: When dividing a large factorial by a smaller
ways a particular set can be factorial, a wide range of values can be cancelled
ordered.For example: When two out
coins are fairly tossed, you can get Factorials basically mean the product of all the
T,T/H,H/T,H/H,T. This means when postive integers after a given number. Example
tossing two coins fairly you have 4 6!= 6 x 5 x 4 x 3 x 2x 1= 720
permutations possible.
PERMUTATIONS
n! Is read as 'n' factorial. This is
used to calculate the
Understanding Permutation of 'n'
permutations of much larger
sets containing lot more data.
distinct objects in a line
Example: How many ways can
the letters in the word
'FREAKY' be arranged ?
First, you will have to count
the number of letters; 6
Second you do 6! And find the
answer to be 720
PERMUTATIONS OF 'k' OBJECTS FROM 'N'
OBJECTS IN A LINE
In some cases, calculating the total number of permutations is bot
needed as just a subset or particular number of terms will be useful.
For example if you were asks the number of permutations possible
using 5 letters of the word 'CAMBRIDGE ', first this formula is needed
N=9
R=5
(9!)\(9-5)!=181440
Therefore, the answer will be 181440
5
CONSTRAINTS ON PERMUTATION
It refers to limitations or conditions that
affects the order of items. This can include:
1- Repetition
2- Fixed positions
3- Subset selections
4- Restrictions
6
PERMUTATION WHEN OBJECTS ARE NOT
DISTINGUISHABLE
WORKED EXAMPLE: Find the number of
This is usually used when permutations of letters in the word, UNAVAILABLE
some items in the set are the
same. For example: in the This will be equal to;
word TRINIDAD, there are 2 `11!\2! X 3!=3326400
d's and 2 I's.
7
COMBINATIONS
Used when the order of
selection does not matter.
Example:
Picking a team of 3 people
from a group of 10. C ( 10 ,
3 ) = 10 ! / ( 7 ! ∗ 3 ! ) = 10 ∗
9 ∗ 8 / ( 3 ∗ 2 ∗ 1 ) = 120 . ...
THANK YOU
Esli Ello Ryan
Year 12 bluebell
Statistics textbook
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