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Q21.

Expert-verified
Found in: Page 635

### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

# 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?

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.

See the step by step solution

## 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 $7×6×5×4×3×2×1=5040$ 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.