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Fundamental Principle of Counting

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Fundamental Principle of Counting - Lesson Summary

If there are three balls of different colours, and three holders, they can be placed in the holders in many different ways.

There are six possible ways of arranging these balls. These are the maximum number of ways in which the three balls can be placed in the holders.

The number of unique ways in which the balls can be arranged is important than the arrangement of the balls.

Consider a situation where a person is at the town hall in our city.  To go to the stadium, he has to board the metro train that takes him to the stadium. There are four ways that go from the town hall to the metro station, and three to go from the metro station to the stadium.

The maximum available routes from the town hall to the stadium are as shown.

Here, each route is unique. 12 routes will take from the town hall to the stadium.

The number of ways using a tree diagram:

Fundamental Principle of Counting or Multiplication Principle

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of the occurrence of the events in the given order is m × n.

This principle can be extended for any number of events.

Let, M: Event of route taken from town hall to metro station.
S: Event of route taken from metro station to stadium.

The number of routes that can be taken from the town hall to the stadium is equal to the product of M and S.

M = 4
S = 3

The number of routes that can be taken from the town hall to the stadium = 4 × 3 = 12.