Institute of Technology of Cambodia
Mathematic Engineering 6
Tutorial 2
Introduction to Probability
1. How many four-letter code words can be formed using a standard 26-letter alphabet
(a) if repetition is allowed?
(b) if repetition is not allowed?
2. Certain automobile license plates consist of a sequence of three letters followed by
three digits.
(a) If no repetitions of letters are permitted, how many possible license plates are
there?
(b) If no letters and no digits are repeated, how many license plates are possible?
3. A combination lock has 40 numbers on it.
(a) How many different three-number combinations can be made?
(b) How many different combinations are there if the three numbers are different?
4. (a) Miss Murphy wants to seat 12 of her students in a row for a class picture. How
many different seating arrangements are there?
(b) Seven of Miss Murphy’s students are girls and 5 are boys. In how many
different ways can she seat the 7 girls together on the left, and then the 5 boys
together on the right?
5. Using the digits 1, 3, 5, 7, and 9 , with no repetitions of the digits, how many
(a) one-digit numbers can be made?
(b) two-digit numbers can be made?
(c) three-digit numbers can be made?
(d) four-digit numbers can be made?
6. There are five members of the Math Club. In how many ways can the positions of
officers, a president and a treasurer, be chosen?
7. (a) A baseball team has nine players. Find the number of ways the manager can
arrange the batting order.
(b) Find the number of ways of choosing three initials from the alphabet if none
of the letters can be repeated. Name initials such as MBF and BMF are
considered different.
8. Find m and n so that C(m, n) = 13
9. The Library of Science Book Club offers three books from a list of 42 . If you circle
three choices from a list of 42 numbers on a postcard, how many possible choices
are there?
10. At the beginning of the second quarter of a mathematics class for elementary school
teachers, each of the class’s 25 students shook hands with each of the other students
exactly once. How many handshakes took place?
Dr. PHAUK Sokkhey
1/2
2021-2022
Institute of Technology of Cambodia
Mathematic Engineering 6
11. There are five members of the math club. In how many ways can the twoperson
Social Committee be chosen?
12. A consumer group plans to select 2 televisions from a shipment of 8 to check the
picture quality. In how many ways can they choose 2 televisions?
13. A school has 30 teachers. In how many ways can the school chocse 3 people to
attend a national meeting?
14. How many different 12-person juries can be chosen from a pool of 20 jurors?
15. A jeweller has 15 different sized pearls to string on a circular band. In how. many
ways can this be done?
16. Four teachers and four students are seated in a circular discussion group. Find the
number of ways this can be done if teachers and students must be seated alternately.
17. A certain shop repairs both audio and video components. Let A denote the event
that the next component brought in for repair is an audio component, and let B
be the event that the next component is a compact disc player (so the event B is
contained in A). Suppose that P (A) = 0.6 and P (B) = 0.05. What is P (B | A) ?
18. Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis
(HGE). Based on a recent study, suppose that 16% of all ticks in a certain location
carry Lyme disease, 10% carry HGE, and 10% of the ticks that carry at least one
of these diseases in fact carry both of them. If a randomly selected tick is found to
have carried HGE, what is the probability that the selected tick is also a carrier of
Lyme disease?
19. If A and B are independent events, show that A0 and B are also independent. [Hint:
First establish a relationship between P (A0 ∩ B) , P (B), and P (A ∩ B).]
20. The Reviews editor for a certain scientific journal decides whether the review for
any particular book should be short (1-2 pages), medium (3-4 pages), or long (5-6
pages). Data on recent reviews indicates that 60% of them are short, 30are medium,
and the other 10% are long. Reviews are submitted in either Word or LaTeX. For
short reviews, 80% are in Word, whereas 50% of medium reviews are in Word and
30% of long reviews are in Word. Suppose a recent review is randomly selected. (a)
What is the probability that the selected review was submitted in Word format?
(b) If the selected review was submitted in Word format, what are the posterior
probabilities of it being short, medium, or long?
Dr. PHAUK Sokkhey
2/2
2021-2022