Combinations, Permutations+Study Notes-Finite Mathematics-M118-9/21/2012
Permutations:
•Permutations are ordered outcomes (order matters)
Select a president, VP and secretary
Combinations:
•Combinations are unordered outcomes (order does not matter)
•Select a committee of 3
Examples:
•How many license plates can be produced using 5 symbols on each plate? The first two
symbols are different letters of the alphabet and the last 3 are different numbers selected
from the digits 0-9. Repetition is not allowed.
•(26,25) 10 x 9 x 8=468,000
■There are 26 letters in the alphabet and they cannot be repeated, so once 1
has been used there is 25 left
■There are 10 numbers available (0,1,2,3,4,5,6,7,8,9) and once 1 is used
there is only 9 left and so on and so on
•In how many ways can 2 men and 2 women be seated in a car that has 2 front seats and 2
rear seats?
•4 x 3 x 2 x 1=24
■There are four people in the problem, and once 1 is seated there are only
3 to seat and so on and so on
Permutations:
•In how many ways can a group of 20 select a president, VP and secretary
•Order matters
•Use the fundamental counting principle (10 x 9 x 8….)
•This is called a permutation of 20 objects taken 3 at a time
■P(20,3)=20 x 19 x 18=6,840
Combinations:
