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