Page 11 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
Some useful tips for counting techniques

When you use counting techniques, you must always keep these in mind: “Do I count everything?” and “Do
I count anything more than once?” to avoid mistakes. It is not easy to answer the question which counting
methods you should use. You may find some of the suggestions below helpful.
1. If the set of elements breaks up into disjoint subsets, then the addition rule can be applied.
2. If the elements are from different sets or the elements to be counted are collected through multiple
steps, then the multiplication rule is used.
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3. Permutations involve choosing a specific number of elements from a set of elements and placing them
in order.
4. Combinations involve choosing a specific number of elements from a set of elements without regard 2
to order.

Exercise 2.1

1. There are two routes from a student’s home to a bus station and three routes from the bus station to
the school. Use the multiplication principle to find the number of ways a journey from the student’s
home to the school via the bus station may be completed.
2. If a Mathematics department schedules 4 lecture sections and 12 tutorial groups for a course in
Introductory Statistics, in how many different ways can a student choose a lecture section and a tutorial
group?
3. In a practical class, students are asked to classify the specimens according to their colours: red, blue,
green, yellow, white and also according to their sizes: small, medium, large and lastly to their gender:
male, female. In how many different ways can a specimen be classified according to colour, size and
gender?
4. Jenny has 9 different blouses and 6 different skirts. Find the number of possible different blouse-skirt
outfits she can form. If she also has 7 pairs of different stockings, how many different blouse-skirt-
and-stocking outfits are possible?
5. The license plates of some cars consist of two letters followed by three digits. Find the number of
possible different license plates if
(a) there is no restrictions,
(b) no letter or digit is repeated.
6. How many lunches are possible consisting of soup, a sandwich, desserts, and a drink if one can select
from 3 soups, 4 types of sandwiches, 4 desserts, and 5 drinks?
7. Find the number of ways for the letters of the word MONDAY to be arranged in a row. How many
different ways can three of these letters be chosen and written in a row if
(a) there is no restriction?
(b) the first letter must be D?
8. How many ways can a football team schedule 3 exhibition games with 3 teams if they are all available
on any of 5 possible dates?

9. How many ways can 8 people be assigned to 2 triple and 1 double rooms?

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02 STPM Math(T) T3.indd 79 28/10/2021 10:21 AM