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

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asked Jul 14, 2023 121k views

4 votes

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

Five students from a 26 -member leadership club will be selected to organize a fundraiser-example-1

Mathematics
college

Zyd asked

by Zyd

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1 Answer

4 votes

Solution

Step 1

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

Step 2:

$\begin{gathered} \frac{26!}{(26\text{ - 5\rparen!5!}} \\ \text{= }\frac{26!}{21!\text{ }*\text{ 5!}} \\ =\text{ }\frac{26\text{ }*\text{ 25 }*\text{ 24 }*\text{ 23 }*\text{ 22 }*\text{ 21!}}{21!\text{ }*\text{ 5 }*\text{ 4}*3*2*1} \\ =\frac{26\operatorname{*}\text{25}*\text{24}*\text{23}*\text{22}}{\text{5}*\text{4}*3*2*1} \\ =\text{ 65780 groups} \end{gathered}$

Final answer

65780

Johny T Koshy answered Jul 19, 2023