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  • A company has 6 job openings and 10 qualified candidates. Each candidate can only be selected for one position. In how many ways can you choose a combination of candidates to fill the job positions

A company has 6 job openings and 10 qualified candidates. Each candidate can only be selected for one position. In how many ways can you choose a combination of candidates to fill the job positions?
 

Option: 1

60


Option: 2

210


Option: 3

720


Option: 4

5040


Answers (1)

best_answer

Since each candidate can only be selected for one position, we can calculate the combinations without repetition. We can use the formula for combinations without repetition:

\mathrm{ C(n, r)=\frac{n !}{(r ! \times(n-r) !) }}

Here, n is the total number of candidates (10) and r is the number of positions to fill (6).

Using the formula, we have:

\mathrm{ C(10,6)=\frac{10 !}{(6 ! \times(10-6) !)} }

Calculating the factorials:

\mathrm{(10-6) !=4 ! }

Calculating the numerator and denominator:

\mathrm{C(10,6)=\frac{5.040}{720} }

Simplifying the fraction:

\mathrm{C(10,6)=720 }

Hence, the 720 , which represents the number of ways to choose a combination of candidates to fill the 6 job positions while ensuring that each candidate is selected for only one position.

Posted by

shivangi.bhatnagar

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