Problem: There are $3$ positions to be filled at a company. There are $7$ male applicants and $6$ female applicants. An applicant can be selected for only one position. For the first position, either a male for a female can be selected. For the second position, a male must be selected. For the third position, a female must be selected. How many different ways are there to select the applicants. Answer: Let $c$ be the count we are seeking. Let $c_1$ be the count of possible applicants assuming we select a male for the first position. Let $c_2$ be the count of possible applicants assuming we select a female for the first position.
\begin c &= c_1 + c_2 \\ c_1 &= 7(6)(6) = 252 \\ c_2 &= 6(7)(5) = 210 \\ c &= 252 + 210 \\ c &= 462 \end Is my solution correct?
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asked Feb 8, 2022 at 23:36
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$\begingroup$ @JMoravitz If you put your comment as an answer, I will accept it and close the question. $\endgroup$
Commented Feb 8, 2022 at 23:47