There are 3 horses (labeled A, B and C) racing for 2 places.

1
Aim What are the permutation and combination?
Do Now
There are 3 horses (labeled A, B and C) racing
for 2 places. 1. In how many ways can the
horses be placed as 1st, 2nd and 3rd?
2. In how many ways can the horses be placed
as 1st and 2nd ?
HW p.685 26,28,45,46,47,49,50,52,53
2
 
This is a permutation
We denote it as 3P3 which is the same as 3!
nPn n! n(n 1)(n 2) 3 2 1
2 3 2 6
This is a permutation
We denote it as 3P2
A permutation is an arrangement of objects in a
specific order.
3
If there are n objects taken n at a time, the
permutation is denoted nPn
nPr is a permutation of n things taken r at a
time. ,where r is less than n
For example The Math Club has 20 members In
how many ways are there of selecting a president,
vice president and secretary?
4
Permutations with repetition
In general, the number of permutations of n
things taken n at a time when a are identical is
In how many ways can 9 letter words be formed
from the word CLASSROOM?
S repeated 2 times and O repeated 2 times.
5
A combination is an arrangement that the order
does not matter.
nCr is a combination of n things taken r at a
time.
There is another notation for combination
For example The Math Club has 20 members How
many committees of 3 members can be selected?
6
How many different arrangement of 5 letters can
be drawn from the alphabet if 3 are consonants
and 2 are vowels?
A local convenient store hires three students to
work. Next month, there are 20 days on which they
will work. Alex will work 8 days, Rosa will work
6 days and Carla will work 6 days. In how many
ways can their schedule for the month be arranged?
7

1. In how many different orders can the program for
   a music recital be arranged if 7 students are to
   perform?

2. In how many ways can 1 junior and 1 senior be
selected from a group of 8 juniors and 6
seniors?
3. A reading list gives the titles of 20 novels
and 12 biographies from which each students
is to choose 3 novels and 2 biographies to
read. How many different combinations of
titles can be chosen?