# Fundamental counting principle

### Fundamental counting principle

The fundamental counting principle can be very helpful when you need to figure out the possible number of outcomes of multiple events. The principle essentially works like this: If there are m possible ways for an event to occur, and n possible ways for another event to occur, there are m x n possible ways for both events to occur. In this lesson, we will apply the principle to real-life scenarios to see how it works.

#### Lessons

• Introduction
Fundamental Counting Principle: In any event involving "AND", the total number of outcomes will be found by "MULTIPLYING".

• 1.
You are packing clothes for a trip. You decide to take three shirts and two pairs of pants:
shirts:
tank top, short sleeve, long sleeve
pants:
skinny jeans, baggy pants

a) How many pieces of clothing are you bringing all together?

b) If an outfit consists of a shirt and a pair of pants, how many different sets of outfit can you make? Determine the answer by using:
(i) a tree diagram
(ii) the fundamental counting principle

• 2.
A summer holiday plan has one item from each category.
Companion : friends, family
Month : May, June, August
Activities : picnic, bike, camp, swim
Transportation : bus, carpool, train
How many different summer holiday plans are possible?

• 3.
A survey has ten multiple choice questions. There are four choices in each question, A, B, C, or D. How many different possible sets of answers are there?

• 4.
Fundamental Counting Principle Involving Restrictions – "restriction must be dealt with first!"
How many odd four digit numbers are there?
An example of a four digit number is 3581, while 0492 is a three digit number.
a)
How many odd four digit numbers are there? An example of a four digit number is 3581, while 0492 is a three digit number.

b)
Now, find out how many odd four digit numbers there are that consist of no repeating digits.

• 5.
Use only the digits 2, 4, 5, 6, 7, 8 and 9 to produce four digit numbers.
a)
How many four digit numbers are there that have no repeating digits?

b)
How many of these numbers are:
i) even? ii) odd? iii) multiples of 5? iv) more than 3000?