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;
[tex]nCr=\frac{n!}{(n-r)!r!}[/tex]
From the question, n = 5 and r = 3. On substituting
[tex]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[/tex]
Hence the number of different ways that three speakers can be selected is 10 ways.
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