Well, organizing a subcommittee can be quite a circus! Let's break it down. Since we must have at least one member who is not a teacher, we can choose one non-teacher from the six available. That gives us 6 choices for one member.
For the remaining three members, we can choose from the entire pool of 11 members, including both teachers and non-teachers. That gives us 11 choices for the second member, 11 choices for the third member, and 11 choices for the fourth member.
To find the total number of distinct subcommittees, we multiply the number of choices for each member together: 6 choices for the first member, multiplied by 11 choices for the second, multiplied by 11 choices for the third, and multiplied by 11 choices for the fourth.
Therefore, the total number of distinct subcommittees is 6 x 11 x 11 x 11 = 8,026.
So, it looks like there are 8,026 different ways to create this subcommittee. That's more options than a clown has colorful wigs!