Review
Answers are on the last slide.
1. A medical researcher needs 6 people to volunteer
to test the effectiveness of an experimental drug.
If 13 people have volunteered for the test, in
how many ways can 6 people be chosen?
2. How many different 4-letter passwords can be
formed from the letters A, B, C, D, E, F, and G
if no repetition of letters is allowed?
3. The model of the car you are thinking of buying
is available in nine different colors and three
different styles (hatchback, sedan, or station wagon).
In how many ways can you order the car?
4. An ice-cream store sells 2 drinks (soda or milk shakes),
in four sizes (small, medium, large, or jumbo), and
five flavors (vanilla, strawberry, chocolate, coffee, or
pistachio). In how many ways can a customer order a
drink?
5. Telephone numbers in the United States begin with
3-digit area codes followed by 7-digit local telephone
numbers. Area codes and local telephone numbers
cannot begin with 0 or 1. How many different
telephone numbers are possible?
6. You and 19 of your friends have decided to form an
internet marketing consulting firm. The group needs
to choose 3 officers – a CEO, an operating manager,
and a treasurer. In how many ways can those
offices be filled?
7. How many ways can you select 6 free videos
from a list of 200 videos?
8. In a race in which there are 50 runners and no ties,
in how many ways can the first three finishers come
in?
9. A 3-person committee is needed to study ways to
improving public transportation. How many
committees could be formed from the 8 people on
the board of supervisor?
10. In poker, a person is dealt 5 cards from a
standard 52-card deck. The order in which you
are dealt 5 cards does not matter. How many different
5-card poker hands are possible?
11. You are taking a multiple-choice test that has 5
questions. Each of the questions has 3 choices,
with 1 correct choice per question. If you select
one of these options per question and leave
nothing blank, in how many ways can you answer
the questions?
12. To win at LOTTO in the state of Florida, one must
correctly select 6 numbers from a collection of
53 numbers (1-53). The order in which the
selection is made does not matter. How many
different selections are possible?
13. A die is rolled once. Find the probability of
getting a number less than 5.
14. If you are dealt one card from a standard
52-card deck, find the probability of being dealt
the king of hearts.
15. Florida’s lottery game, LOTTO, is set up so that each
player chooses six different numbers from 1 to 53.
If the 6 numbers chosen match the 6 numbers
drawn randomly twice weekly, the player wins (or
shares) the top prize. With one LOTTO ticket, what
is the probability of winning the prize?
16. In 2001, Americans spent nearly 18 billion
dollars on lotteries set up by revenue-hungry
states. If a person buys 5000 different tickets in
Florida’s LOTTO, (refer to previous problem), what
is his probability of winning?
17. What is the probability of a family having 9 girls in
a row?
ANSWERS
1) 1716
2) 840
3) 27
4) 40
5) 6,400,000,000
6) 6840
7) 8.24 x 10^10
8) 117,600
10) 2,598,960
9) 56
11) 243
14) 1/52
12) 22,957,480
15) 1/22,957,480
16) 5000/22,957,480
17) 1/512
13) 2/3