Questions: A group of five entertainers will be selected from a group of twenty entertainers that includes Small and Trout. In how many ways could the group of five include at least one of the entertainers Small and Trout? A. 8568 ways B. 6936 ways C. 15,504 ways D. 11628 ways

Solution Steps

To solve this problem, we can use the concept of combinations. First, calculate the total number of ways to select 5 entertainers from 20. Then, calculate the number of ways to select 5 entertainers without including Small and Trout. Subtract the latter from the former to find the number of ways to include at least one of Small or Trout.

To find the total number of ways to select 5 entertainers from a group of 20, we use the combination formula:

\[ \binom{20}{5} = 15504 \]

Next, we calculate the number of ways to select 5 entertainers from the 18 who are not Small or Trout:

\[ \binom{18}{5} = 8568 \]

To find the number of ways to include at least one of Small or Trout, we subtract the number of ways to select 5 entertainers without them from the total number of ways:

\[ 15504 - 8568 = 6936 \]

Final Answer