Answered

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There are 19 students in a homeroom. How may different ways can they be chosen tobe elected President, Vice President, and Treasurer?

Sagot :

The number of students in a homeroom is

[tex]n=19[/tex]

The number of posts to be chosen from is

[tex]r=3[/tex]

Concept:

The above selection can be done using the permutation formula below

[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

By substituting the values, we will have

[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ ^{19}P_3=\frac{19!}{(19-3)!} \\ ^{19}P_3=\frac{19!}{16!} \end{gathered}[/tex]

By expanding the factorial, we will have

[tex]\begin{gathered} ^{19}P_3=\frac{19!}{16!} \\ ^{19}P_3=\frac{19\times18\times17\times16!}{16!} \\ ^{19}P_3=19\times18\times17 \\ ^{19}P_3=5814\text{ ways} \end{gathered}[/tex]

Hence,

The final answer is = 5,814 ways

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