Four accounting majors, two economics majors, and three marketing majors have interviewed for five different managerial positions with a large company. Find the number of different ways that five of these people could be hired if the first two positions are to be filled by an accounting manager and an assistant accounting manager, the third position is to be filled by an economics manager, and the last two positions are to be filled by a marketing manager and an assistant marketing manager.
There are 4P2 = 12 ways to fill the accounting positions
There are 2P1 = 2 ways to fill the economics position
There are 3P2 = 6 ways to fill the marketing positions
So, there are 12*2*6 = 144 ways to fill the positions.
Ah, the joy of hiring managers. Let's break it down:
To fill the first position of an accounting manager, there are 4 options. After that, for the assistant accounting manager position, there are 3 options remaining.
Moving on to the economics manager position, there are 2 options available from the 2 economics majors.
Finally, for the marketing manager position, there are 3 options from the 3 marketing majors, and for the assistant marketing manager position, there are 2 options from the remaining 2 marketing majors.
To find the total number of different ways to hire for these positions, you just need to multiply the number of options for each position:
4 options for the accounting manager * 3 options for the assistant accounting manager * 2 options for the economics manager * 3 options for the marketing manager * 2 options for the assistant marketing manager = 4 * 3 * 2 * 3 * 2 = 144
So, there are 144 different ways to hire the managers for these positions. Good luck finding the perfect team!
To solve this problem, we can break it down into steps and calculate the number of possibilities for each step.
Step 1: Select an accounting manager
There are 4 accounting majors, and we need to select 1. The number of possibilities is 4.
Step 2: Select an assistant accounting manager
After selecting the accounting manager in step 1, there are 3 remaining accounting majors. We need to select 1. The number of possibilities is 3.
Step 3: Select an economics manager
There are 2 economics majors, and we need to select 1. The number of possibilities is 2.
Step 4: Select a marketing manager
There are 3 marketing majors, and we need to select 1. The number of possibilities is 3.
Step 5: Select an assistant marketing manager
After selecting the marketing manager in step 4, there are 2 remaining marketing majors. We need to select 1. The number of possibilities is 2.
To calculate the total number of possibilities, we multiply the number of possibilities for each step together:
Total possibilities = 4 * 3 * 2 * 3 * 2
Total possibilities = 144
Therefore, there are 144 different ways that five of these people could be hired for the given positions.
To solve this problem, we need to consider the number of ways to fill each position separately and then multiply them together.
1. Accounting positions:
- The first position, accounting manager, can be filled by any one of the four accounting majors.
- The second position, assistant accounting manager, can be filled by any one of the remaining three accounting majors.
- Therefore, the number of ways to fill the accounting positions is 4 * 3 = 12.
2. Economics position:
- The third position, economics manager, can be filled by any one of the two economics majors.
- Therefore, the number of ways to fill the economics position is 2.
3. Marketing positions:
- The fourth position, marketing manager, can be filled by any one of the three marketing majors.
- The fifth position, assistant marketing manager, can be filled by any one of the remaining two marketing majors.
- Therefore, the number of ways to fill the marketing positions is 3 * 2 = 6.
Now, we can calculate the total number of ways to hire five people for these positions by multiplying the number of ways for each position together:
Total number of ways = (Number of ways to fill accounting positions) * (Number of ways to fill economics position) * (Number of ways to fill marketing positions)
Total number of ways = 12 * 2 * 6 = 144.
Therefore, there are 144 different ways that five people can be hired for these managerial positions.