Fundamental principle of counting

The Fundamental principle of counting (or Multiplication principle) states that:
"If an event can occur in mm different ways, following which another event can occur in nn different ways, then the total number of occurrence of the events in the given order is m×nm \times n."


Example:
If you have 3 trousers and 2 shirts, in how many ways can you dress up?

Soln. In order to dress up, you will have to select a trouser and a shirt each. Since you have 3 trousers, you can select a trouser in 3 ways. Similarly, you can select a shirt in 2 ways.
Now, as per the multiplication principle, the total number of ways in which you can select a trouser as well as a shirt is 3×2=63 \times 2 = 6. So, you can dress up in 6 different ways.
(Answer: 6)


The above principle can be generalised for any finite number of events.
For example, for 3 events, the principle is as follows:
"If an event can occur in mm different ways, following which another event can occur in nn different ways, following which a third event can occur in pp different ways, then the total number of occurrence to the events in the given order is m×n×pm \times n \times p."

Practice:
Exercise 1 (Bike purchase)

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