Question

The members of the Student Activity Council on your campus are meeting to select three speakers for a​ month-long event celebrating artists and entertainers.The first names of the choices are Ben, Will, Stewart, Hilary and Kate. How many different ways can the three speakers be​ selected?

Answer 1

The number of different ways that three speakers can be​ selected is 10 ways

Given the names of choice to be Ben, Will, Stewart, Hilary, and Kate. This means that we have a total of 5 name choices.

If the members of students activities are to select three speakers among these people, the number of ways this can be done is by using the combination rule as shown;

$nCr=\frac{n!}{(n-r)!r!}$

From the question, n = 5 and r = 3. On substituting

$5C3=\frac{5!}{(5-3)!3!}\\5C3=\frac{5!}{2!3!}\\5C3=\frac{5 \times 4 \times 3!}{2 \times 3!} \\5C3=\frac{20}{2}\\5C3 = 10 ways$

Hence the number of different ways that three speakers can be​ selected is 10 ways.

Learn more here: brainly.com/question/24145745