# (b) Explain principle of multiplication with an example.

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The principle of multiplication is a fundamental concept in combinatorics and probability theory. It states that if there are $$n_1$$ ways to do one thing and $$n_2$$ ways to do another, then there are $$n_1 \times n_2$$ ways to do both.

Mathematically, if an event E1 can occur in $$n_1$$ ways, and for each of these ways, an event E2 can occur in $$n_2$$ ways, then the total number of ways both events E1 and E2 can occur together is $$n_1 \times n_2$$.

For example, let's consider two events:

- Event E1: Rolling a fair six-sided die and getting an even number.

- Event E2: Tossing a fair coin and getting heads.

Event E1 can occur in three ways (rolling a 2, 4, or 6), and event E2 can occur in two ways (getting heads or tails). According to the principle of multiplication, the total number of ways both events can occur together is $$3 \times 2 = 6$$. These ways are: (2, H), (2, T), (4, H), (4, T), (6, H), (6, T).

This principle is widely used in counting problems where the occurrences of different events are independent of each other. The total number of outcomes for a sequence of independent events is the product of the number of outcomes for each individual event.