A president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. how many different choices of officers are possible if?

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01-09-2022
Social Studies

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A president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. how many different choices of officers are possible if?

Sagot :

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tutorconsortium203 tutorconsortium203 · Answer 1 · 2022-09-05T17:38:12-04:00

A president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. Then, the total possible combinations be 720 without repetition.

What is combination?

Selections are another name for combinations. Combinations are the selection of items from a specific set of items.

We do not plan to arrange anything here.
We intend to choose them.
The combinations equation is used to quickly determine the number of distinct groups of r objects that can be founded from the obtainable n different objects.
The factorial of n divided by the product of a factorial of r and the factorial of a difference of n and r is the formula for combinations.

Now according to the question;

A president, treasurer, and secretary are to be choose from 10 people.

Suppose president is selected first.

Thus, there are 10 president who can be selected for president.

Once president is selected 9 positions are left.

Suppose we select treasurer after this. So, we have 9 persons for that.

Now, 8 persons are left for the secretary position.

So, this could be done by 1 out of remaining 8 persons.

Thus, the selection combination will be as follows.

= 10×9×8

= 720.

Therefore, the number of ways in which a president, treasurer, and secretary all chosen from club of 10 people are 720.

To know more about the combinations, here

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Sagot :

What is combination?

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