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We can select the President, Vice-President and Secretary from a pool of 7 qualified candidates in 35 different combinations.
As per question statement, the President, Vice-President and Secretary are to be selected from a pool of 7 qualified candidates.
We are required to calculate the number of combinations in which we can select the President, Vice-President and Secretary are to be selected from a pool of 7 qualified candidates.
To solve this question, we need to know the formula of Combination which goes as [tex](nCr)=\frac{n!}{r!(n-r)!}[/tex] , i.e., we are to select a set or "r" from a set of "n".
Here, we have to select the President, Vice-President and Secretary from a pool of 7 qualified candidates, i.e., 3 people are to be selected from a set of 7.
Therefore applying (nCr) formula with (n = 7) and (r = 3), we get,
[tex](7C3)=\frac{7!}{3!(7-4)!} =\frac{7!}{3!4!} =\frac{4!*5*6*7}{(2*3)*4!}=\frac{5*6*7}{6}=(5*7)=35[/tex].
- Combinations: In mathematics, a combination is a method of selecting items from a set, where the order of selection does not matter, i.e., if we have a set of three numbers P, Q and R, then in how many ways we can select two numbers from each set, can be easily defined by combination.
To learn more about combinations, click on the link below.
https://brainly.com/question/8561440
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