There are 4000 students at Mountain High School, and 3/8 of these students are seniors. If 1/6 of the seniors are in favor of the school forming a debate team and 3/5 of the remaining students (not seniors) are also in favor of forming a debate team, how many students do not favor this idea?

First, we need to find out how many seniors there are at Mountain High School. We know that 3/8 of the 4000 students are seniors, so we can calculate:

Number of seniors = (3/8) * 4000

Number of seniors = 1500

Next, we need to find out how many seniors are in favor of forming a debate team. We're told that 1/6 of the seniors are in favor, so we can calculate:

Number of senior in favor = (1/6) * 1500

Number of senior in favor = 250

Now, we need to find out how many non-senior students are in favor of forming a debate team. We know that 3/5 of the remaining students (not seniors) are in favor, so we can calculate:

Number of non-senior in favor = (3/5) * (4000 - 1500)

Number of non-senior in favor = (3/5) * 2500

Number of non-senior in favor = 1500

Finally, to find out how many students do not favor this idea, we can subtract the total number of students in favor from the total number of students:

Total students = 4000

Total students in favor = 250 + 1500 = 1750

Number of students not in favor = Total students - Total students in favor

Number of students not in favor = 4000 - 1750

Number of students not in favor = 2250

So, there are 2250 students who do not favor the idea of forming a debate team.