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2 November, 10:39

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?

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  1. 2 November, 10:55
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    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.
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