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A club with nine members is to choose three​ officers: ​ president, vice-president, and​ secretary-treasurer. If each office is to be held by one person and no person can hold more than one​ office, in how many ways can those offices be​ filled?

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thaswasupbreh
You would do 9*8*7 because any 9 could take up one then 8 people are left for the other and  7 for the final one so 504 ways

As per permutation, in 504 different ways those offices can be​ filled.

What is the permutation for a given data set?

"A permutation is an arrangement of objects in a definite order."

Given, the club with nine members is to choose three​ officers.

If each office is to be held by one person and no person can hold more than one​ office.

Therefore, the number of ways those offices can be filled is

[tex]= P^{9}_{3} \\= \frac{9!}{(9-3)!}\\= \frac{9!}{6!}\\= \frac{(9)(8)(7)(6!)}{6!}\\= (9)(8)(7)\\= 504[/tex]

Learn more about permutation here: https://brainly.com/question/1216161

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