Darren's elementary school principal wants to hire some new teachers. 3 teachers applied for one 1st grade teaching job, and 10 teachers applied for one 2nd grade teaching job. There is also a job opening for a 3rd grade teacher, and 10 teachers applied for the job. How many different ways can Darren's principal hire new teachers?
ways
There are a few different cases to consider:
Case 1: 1st grade job
There are 3 applicants for the 1st grade job, and only 1 can be hired. Therefore, there are 3 ways to hire for this job.
Case 2: 2nd grade job
There are 10 applicants for the 2nd grade job, and only 1 can be hired. Therefore, there are 10 ways to hire for this job.
Case 3: 3rd grade job
There are 10 applicants for the 3rd grade job, and only 1 can be hired. Therefore, there are 10 ways to hire for this job.
Overall, the hiring for each job is independent of the others. Therefore, the total number of ways to hire all three teachers is:
3 x 10 x 10 = 300
So there are 300 different ways for Darren's principal to hire new teachers.