PERMUTATIONS vs. COMBINATIONS
WARM-UP QUESTION
Students at OLMC elect a student council.
a)
If Barney, Betty, Fred and Wilma are all on the council, determine
the number of ways that they can fill the positions of president,
vice-president and secretary.
List all the possibilities below.
b)
If instead, a committee of three must be chosen with no specific
positions assigned, determine the number of ways Barney, Betty,
Fred and Wilma can form this committee.
The number of possible ordered choices is _____________________.
The number of ways of arranging 3 objects is ___________________.
The number of possible unordered choices is __________________.
When selecting elements, order may or may not be important.
permutation: an ordered selection of elements
combination: an unordered selection of elements
COMBINATION NOTATION (C-notation)
COMBINATION NOTATION:
nC r
= C(n,r)
“ n choose r ”
 n
=  
NOTE:
r
n!
=
(n  r )! r !
n
Cr 
P
r!
n r
where C(n,r) is the number of combinations
of n objects taken r at a time and 0  r  n.
For example, 8 C6 = C(8,6)
8!
=
2!6 !
= 28
EXAMPLE #1
a)
18
C 15 =
Evaluate each of the following:
8
b)   =
5
EXAMPLE #2
Determine the number of ways a team of six
volleyball players can be chosen from a roster of
eleven.
EXAMPLE #3
Determine the number of ways a prom committee
consisting of 2 teachers and 4 students can be
chosen if there are 5 teachers and 11 students
interested in serving on the committee.