Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these could be hired.
One accounting major, one economics major, and one marketing major would be hired, then the two remaining positions would be filled by any of the majors left.
a. 720 ways b. 2160 ways c. 48 ways d. 4320 ways
720
720
To solve this problem, we can break it down into two parts:
1. Selecting one accounting major, one economics major, and one marketing major for the first three positions.
2. Filling the remaining two positions with any of the remaining candidates.
For the first part, we have:
- 4 options for selecting one accounting major out of the four available.
- 2 options for selecting one economics major out of the two available.
- 3 options for selecting one marketing major out of the three available.
This gives us a total of 4 * 2 * 3 = 24 options for the first three positions.
For the second part, we have:
- 4 candidates remaining after choosing one accounting major.
- 1 economics major left after choosing one for the first three positions.
- 2 marketing majors left after choosing one for the first three positions.
Since the order in which the two remaining positions are filled does not matter, we can calculate the number of ways to fill them using combinations. We need to select 2 candidates out of the remaining 4 (accounting and marketing majors combined), so we have:
- 4 options for the first position out of the remaining candidates.
- 3 options for the second position out of the remaining candidates.
This gives us a total of 4 * 3 = 12 options for the remaining two positions.
To find the total number of ways to hire five candidates, we multiply the number of options for the first three positions by the number of options for the remaining two positions, which gives us 24 * 12 = 288 ways.
Therefore, the correct answer is not listed among the provided options.
To solve this problem, we need to break it down into two parts:
Part 1: Selecting one accounting major, one economics major, and one marketing major
There are four accounting majors, two economics majors, and three marketing majors competing for these positions. To compute the number of ways to choose one from each major, we multiply the number of options for each major together:
Number of options for accounting major = 4
Number of options for economics major = 2
Number of options for marketing major = 3
Now, multiply these numbers together: 4 * 2 * 3 = 24.
Part 2: Selecting the remaining two positions with any of the majors left
After selecting one accounting major, one economics major, and one marketing major, there are still two positions remaining to be filled. The remaining candidates can be from any of the original three majors since we have already selected one from each major. Therefore, we have three options for each of the two remaining positions.
Number of options for the first remaining position = 3
Number of options for the second remaining position = 3
To find the total number of ways to fill these two remaining positions, we multiply the number of options together: 3 * 3 = 9.
To find the total number of ways to hire five candidates for these positions, we multiply the number of ways in part 1 by the number of ways in part 2:
24 * 9 = 216.
Therefore, the answer is b) 2160 ways.