Q21. - Algebra 2

Question

In how many orders can eight actors be listed in the opening credits of a movie if the leading actor must be listed first or last?

Step-by-Step Solution

Answer

There are 10080 orders the eight actors can be listed in the opening credits of a movie if the leading actor must be listed first or last.

Step 1. Given Information.

It is to be determined in how many orders can eight actors be listed in the opening credits of a movie if the leading actor must be listed first or last.

Step 2. Calculation .

Since the leading actor must be listed first or last, considering that leading actor is first, the remaining 7 actor listing are to be arranged.

 

When one of the 7 actors is listed, 6 remain to be listed in the next place, then 5 and so on.

 

By the Fundamental Counting Principle, there are $7\times 6\times 5\times 4\times 3\times 2\times 1=5040$ different orders the 7 actors can be listed if the leading actor is considered to be listed first.

Similarly, when the leading actor is listed last there are 5040 more orders.

Step 3. Conclusion .

Hence, by Fundamental Counting Principle, there are 10080 orders the eight actors can be listed in the opening credits of a movie if the leading actor must be listed first or last.