Question

Five students from a 26 -member leadership club will be selected to organize a fundraiser. How many groups of 5 students are possible?

Answer 1

Solution

Step 1

$^{26}C_5\text{ = }\frac{26!}{(26-5)!5!}\text{ groups}$

Step 2:

$\begin{gathered} \frac{26!}{(26\text{ - 5\rparen!5!}} \\ \text{= }\frac{26!}{21!\text{ }\times\text{ 5!}} \\ =\text{ }\frac{26\text{ }\times\text{ 25 }\times\text{ 24 }\times\text{ 23 }\times\text{ 22 }\times\text{ 21!}}{21!\text{ }\times\text{ 5 }\times\text{ 4}\times3\times2\times1} \\ =\frac{26\operatorname{\times}\text{25}\times\text{24}\times\text{23}\times\text{22}}{\text{5}\times\text{4}\times3\times2\times1} \\ =\text{ 65780 groups} \end{gathered}$

Final answer

65780