If a first experiment can be performed in 5 distinct ways and a second experiment can be performed in 9 distinct ways, the two experiments together can be performed in how many distinct ways?

11.4#3

The number of ways the two experiments together can be performed is;

45 ways

We are told that;

Number of distinct ways of performing a first experiment = 5 ways

Number of distinct ways of performing a second experiment = 9 ways

Since the two experiments are both distinct, then it means they are both independent events.

Thus, the number of ways of both of them being performed in distinct ways will be the product of the distinct number of ways.

Thus;

number of ways the two experiments together can be performed = 9 × 5 = 45 ways

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The two experiments together can be performed in 45 distinct ways.

Step-by-step explanation:

Number of distinct ways to perform first experiment = 5

Number of distinct ways to perform first experiment = 9

For each distinct way the first experiment is performed there are 9 distinct ways to perform the second experiment. Also, the way each experiment is performed is independent of the other experiment (important assumption).

So, according to the fundamental rule of counting the total number of ways to perform both the experiments must be equal to the product of number of ways in which each experiment can be performed.

Therefore, the two experiments can be performed together in 5 x 9 = 45 distinct ways.

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