Princeton Review
To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?
A. 1,490
B. 132
C. 120
D. 60
E. 23
OA C.
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To fill a number of vacancies, an employer must hire 3
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Number of ways to choose 3 programmers from 6 applicants = 6C3 = (6*5*4)/(3*2*1) = 20.AAPL wrote:Princeton Review
To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?
A. 1,490
B. 132
C. 120
D. 60
E. 23
Number of ways to choose 2 managers from 4 applicants = 4C2 = (4*3)/(2*1) = 6.
To combine the options above, we multiply:
20*6 = 120.
The correct answer is C.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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This is a combination problem since the order of selecting the applicants for each job title does not matter.AAPL wrote:Princeton Review
To fill a number of vacancies, an employer must hire 3 programmers from among 6 applicants and 2 managers from among 4 applicants. What is the total number of ways in which she can make her selection?
A. 1,490
B. 132
C. 120
D. 60
E. 23
3 programmers from 6 applicants can be hired in 6C3 ways:
6C3 = 6!/3!(6-3)! = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2 x 1) = 20
2 managers from 4 applicants can be hired in 4C2 ways:
4C2 = 4!/2!(4-2)! = (4 x 3)/2! = (4 x 3)/(2 x 1) = 6
Thus, the total number of ways in which she can make her selection is 20 x 6 = 120.
Answer: C
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