if a first experiment can be performed in 5 distinct ways and a second experiment can be performed in 2 distinct ways, the two experiments together produce how many distinct outcomes?

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.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right