Download 10C5 - QC Economics

Geordan Hull
Queens College
Economics 249
Spring 2006
Combinations and Permutations
Combinations and Permutations both provide you with the total amount of outcomes. The
difference between the two is that "order" matters for Permutations. Presuming that N and n are
the same for a given Combination and Permutation example, the Permutation will give you the
larger answer. This is because you will have more possible outcomes (possibilities) when order
is considered.
Hint: In fractions with equal numerators (top number), the fraction with the smallest denominator
(bottom number) will be the largest and the fraction with the largest denominator will be smallest
(e.g. 1/2 > 1/3). When N and n are the same for a given Combination and Permutation example,
the denominator will always be bigger in the Combination than in the Permutation, resulting in a
smaller number.
Example:
In a group of ten people, how many different groups of five can be formed a) when order is not a
factor and b) when order is a factor?
a)
10C5
= 10!/[5!(10-5)!]
= (10*9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)(5*4*3*2*1)
= 3,628,800/(120*120)
= 252
Or
= (10*9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)(5*4*3*2*1)
--> The bold numbers will cancel out
= (10*9*8*7*6)/(5*4*3*2*1)
= 252
b)
10P5
= 10!/(10-5)!
= (10*9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)
= 3,628,800/120
= 30,240
Or
= (10*9*8*7*6*5*4*3*2*1)/(5*4*3*2*1)
--> The bold numbers will cancel out
= (10*9*8*7*6)
= 30,240