Aim: How do we use permutation and

1
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
2
a. 10 choices select any 4 is a combination of
b is a compound events.
c is also a compound events.
3
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.
4
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)
5
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?
P(E) n(E)/n(S)
6
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.
7
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?
The letters of the word TOMATO are arranged at
random. What is the probability that the
arrangement begins and ends with T?