Everything Maths Grade 12

12.5 CHAPTER 12. COMBINATIONS AND PERMUTATIONS

will have a total of n 1 × n 2 possible outcomes. Thisidea can be generalisedto m experiments as the
total number of outcomes for m experiments is:

n 1 ×n 2 ×n 3 ×···×nm=

�m

i=1

ni

�

is the multiplication equivalent of

�

Note: the order in which the experiments are done does not affect thetotal number of possibleout-
comes.

Example 1: Lunch Special

QUESTION

A take-away has a 4-piece lunch special which consists of a sandwich, soup, dessert and drink

for R 25 , 00. They offer the following choices for :

Sandwich: chicken mayonnaise, cheese and tomato, tuna, and ham andlettuce

Soup: tomato, chicken noodle, vegetable

Dessert: ice-cream, piece of cake

Drink: tea, coffee, coke,Fanta and Sprite.

How many possible meals are there?

SOLUTION

Step 1 : Determine how many parts to the meal there are

There are 4 parts: sandwich, soup, dessert and drink.

Step 2 : Identify how many choices there are for each part

Meal component Sandwich Soup Dessert Drink

Number of choices 4 3 2 5

Step 3 : Use the fundamental counting principle to determine how many different meals

are possible

4 × 3 × 2 × 5 = 120

So there are 120 possible meals.

12.5 Combinations

EMCDI

The fundamental counting principle describeshow to calculate the total number of outcomeswhen
multiple independent events are performed together.