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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 :

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

https://brainly.com/question/1757772

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