Respuesta :
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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