Question

A club with thirteen 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?

Answer 1

Answer:

hope this helps

Step-by-step explanation:

so there are 10 choices for president

then after that there are 9 choices for VP

then afte P and VP there are 8 choices for Treasurer

and finally after P, VP and T, there are 7 choices left for Secretary.

So the number of ways to fill those offices with 10 candidates is

Answer 2

There are 720 possible ways.

Permutation and combination:

• A permutation is an act of arranging the objects or numbers in order.
• Combinations are the way of selecting the objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

President:

• The President picks the leaders of all government agencies, including the Cabinet, in order to carry out and enforce the laws passed by Congress.
• The Vice President is a member of the Executive Branch and is prepared to take over as President if necessary.

Vice-President:

• The only constitutional obligation for a vice president is to preside over the Senate, except for taking over as president in the event of a president's demise or resignation.
• Vice presidents are not permitted to cast a vote in the Senate, with the exception of breaking a tie or addressing the Senate informally without the consent of the senators.

Solution -

There are 10 alternatives for the presidency, 

9 options for vice president, and

8 options for secretary and treasurer.

In all, $10$ × $9$ × $8 = 720$ possible ways.

Therefore, there are 720 possible ways.

Know more about Permutation and combination here:

https://brainly.com/question/4658834

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