Page 12 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
10. A club has 30 members. They are to select 3 office holders consisting of the president, secretary, and
treasurer for the following year. They always select these office holders by drawing 3 names randomly
from names of all members. The first person selected becomes the president, the second is the secretary,
and the third takes over as treasurer. Thus, the order in which 3 names are selected is important. Find
the total arrangements of 3 names from 30.

11. Find the number of permutations that can be formed from the letters of the word POPULAR. How
many of these permutations,
(a) begin and end with P?
(b) have the two P’s separated?
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(c) have the vowels together?
2 12. (a) In how many different ways can a student answers 8 true-false questions?
(b) In how many ways may the test be completed if a student is imposed for each incorrect answer,
so that the student may leave some questions unanswered?
13. An ice cream parlour has seven flavours of ice cream. Nathan wants to buy two flavours of ice cream.
If he randomly selects two flavours out of seven, how many possible combinations are there?
14. Consider the collection of objects consisting of the five letters c, d, e, f, g.
(a) List all possible combinations of three letters from this collection of five letters.
(b) Use part (a) to determine the number of possible combinations of three letters that can be formed
from this collection of five letters.
(c) Use combination formula to confirm the answer obtained in part (b).
15. To recruit new members, a compact-disc (CD) club advertises a special introductory offer:
A new member agrees to buy one CD at regular club prices and receives free any four CDs of the
member’s choice from a collection of 50 CDs. Find the number of possibilities a new member has for
the selection of the four free CDs.

16. In how many different ways can a coach choose two badminton players from among seven students
and three table tennis players from among nine students?
17. Evaluate
(a) 5 P 5 (b) P 3 (c) 6 P 4 (d) 12 P 0
8
(e) 7 C 4 (f) 10 C 10 (g) 9 C 5 (h) 15 C 0
18. Out of 5 class representatives and 7 prefects, a committee consisting of 2 class representatives and 3
prefects is to be formed. In how many ways can this be done if,
(a) any class representative and any prefect can be included,
(b) one particular prefect must be in the committee, and
(c) two particular class representatives cannot be in the committee.

19. Santi has 6 flowers, each of a different variety. How many different bouquets can she form?
20. There are 25 paintings in a collection. How many ways can the following groups be selected?
Write the answers in factorial notations.
(a) 5 paintings,
(b) 20 paintings
What conclusion can you deduce from parts (a) and (b)?
21. A developer of a residential subdivision has four house styles and wants to build on eight adjacent
lots. How many distinguishable arrangements are possible if the developer decides to build two houses
of each style?
22. A school has 4 Mathematics teachers, 3 Chemistry teachers and 2 Biology teachers. Find the number
of different sets of teachers a student could have for these 3 subjects.

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02 STPM Math(T) T3.indd 80 28/10/2021 10:21 AM