Aim: How do we use permutation and
combination to evaluate probability?
Do Now: Your investment counselor has
placed before you a portfolio of 6
stocks and 4 bonds. Following her
advice, you have decided to invest in
4 of the ten choices. In how many
ways can you
a. select any 4?
b. select two stocks and two bonds?
c. select 3 stocks and 1 bond?
HW: Worksheet
a. 10 choices select any 4 is a combination of
10
C4  210
b is a compound events. 6 C 2  4 C 2  15  6  90
c is also a compound events.
6
C3  4 C1  20  4  80
Your investment counselor has placed before
you a portfolio of 6 stocks and 4 bonds.
4 investments are selected at random from 10
ten choices. Find the probability of
a) selecting two stocks and two bonds.
b) selecting three stocks and one bond.
To handle this type of problem, we need to
use the combination to find the all the possible
ways in a certain event over the total number
of ways in the sample space.
n( E )
P( E ) 
n( S )
n(E): Count the total number of outcomes in the sample space.
n(S): Count all the possible outcomes in the event E.
a)
b)
6
C2 4 C2 15  6 90 3



210 210 7
10 C 4
6
C3 4 C1 20  4 80
8



210 210 21
10 C4
A homeowner plants 6 bulbs selected at
random from a box containing 5 tulip bulbs and
4 lilac bulbs. What is the probability that he
planted 4 tulip bulbs and 2 lilac bulbs?
5
C 4  4 C 2 5  6 30



P(E) = n(E)/n(S) =
84 84 14
9 C6
5
An urn contains 4 white marbles and 5 blue
marbles. If 3 marbles are drawn at random with
no replacement, what is the probability that at
least 2 marbles drawn are blue?
3 marbles are drawn, at least 2 blue marbles means
either 2 blue and 1 white, or 3 are blue 0 are white.
Therefore, n(E) is consisted of n(A) and n(B), where
n(A) = combination of 2 blue and 1 white marbles,
and n(B) = the combination of 3 blue and 0 white
marbles.
n( A)  n( B)
P( E ) 
5
n( S )
C2 4 C1  5 C3 4 C0 40  10 50 25



84
84 42
9 C3
The letters of the word CABIN are arranged at
random. What is the probability that one
arrangement chosen at random will begin and
end with a vowel? 2  3!1 2  6
12
1
5!

120

120

10
The letters of the word TOMATO are arranged
at random. What is the probability that the
arrangement begins and ends with T?
4!
24
1  1 1  1
2!  2  12
6!
720
180
2!2!
4