Hi. I hope that you now have some idea of the multiplication principle. This lesson will be focused on another basic principle of counting, known as the Addition Principle.

## The Addition Principle

Let’s start with a simple problem: Suppose there are 3 different flights and two different trains connecting two places A and B. In how many ways can you reach from A to B (using only these flights or trains)?

The answer seems obvious: 5

Why? Because you can **either **choose one of the flights (3 choices) **or **choose one of the trains (2 choices). Therefore the total number of choices are 3 + 2 = 5 (Flight 1 **or** Flight 2 **or** Flight 3 **or** Train 1 **or **Train 2)

Another one: A restaurant offers 4 non-veg dishes and 3 veg dishes as starters. How many different types of starters does the restaurant offer?

Again, the answer will be 4 + 3 = 7.

So what is the addition principle about? Here is one way to state it:

“If two events A_{1} and A_{2} can occur in m and n ways respectively (none of these being common), then **either** of these events can occur in m + n ways.”

An analogous statement for the multiplication principle will be:

“If two events A_{1} and A_{2} can occur in m and n ways respectively, then **both** of these events can occur together in m x n ways.”

## Lesson Summary

The addition principle states that:

“If two events A_{1} and A_{2} can occur in m and n ways respectively (none of these being common), then **either** of these events can occur in m + n ways.”

In the next part of the lesson, we’ll see some cases when these principles cannot be applied directly, and how we can combine these two principles for such cases.

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