In a task, you can choose between two exclusive alternatives A or B, where the first alternative A can be completed in m ways and the second alternative B can be completed in n ways. Then in how many different ways can this task be completed?

The total number of ways to complete the task is (m + n) ways.

Step-by-step explanation:

Exclusive alternatives A or B implies that only one of the two can be fulfilled.

That is, either alternative A or B can be carried out, not both.

n (A and B) = 0

The number of ways of doing the task if alternative A is selected is m ways.

The number of ways of doing the task if alternative B is selected is n ways.

As the alternatives A and B are exclusive the number of ways to complete the task is:

Number of ways to complete the task = n (A) + n (B) - n (A and B)

= m + n - 0

= m + n

Thus, the total number of ways to complete the task is (m + n) ways.