4 accounting majors, 2 economics majors, and 3 marketing majors have interviewed for 5 different positions with a large company. Find the number of different ways that 5 of these could be hired. The 4 accounting majors muust be hired first, and then the final position would be chosen from the remaining majors.

To solve this problem, we need to consider two steps:

Step 1: Hire the accounting majors
Since there are 4 accounting majors, all of them must be hired for one of the positions. The order in which they are hired does not matter, so we can use combinations to calculate the number of ways to hire them.

The formula for combinations is: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to choose.

Using this formula, we have:
n = 4 (accounting majors)
r = 4 (positions)

The number of ways to hire the 4 accounting majors is:
4C4 = 4! / (4!(4-4)!) = 1

Step 2: Choose the last position from the remaining majors
Once the 4 accounting majors are hired, there are 5 remaining candidates for the last position. Those candidates include 2 economics majors and 3 marketing majors. Again, the order in which they are hired does not matter, so we can use combinations.

n = 5 (remaining majors)
r = 1 (position)

The number of ways to choose 1 candidate from the remaining majors is:
5C1 = 5! / (1!(5-1)!) = 5

To find the total number of ways to hire 5 candidates while considering the given conditions, we multiply the results from both steps:
1 * 5 = 5

Therefore, there are 5 different ways that 5 candidates can be hired, with the condition that the 4 accounting majors are hired first and the final position is chosen from the remaining majors.