I am a woodworker, and am designing a two part magnetic/spring lock for my blanket chest. The first part has 3 master buttons (primary buttons A, B, C), and the second part has 11 secondary buttons (1, 2, 3, ....11). What you do first is choose one of the three master buttons. Then out of the secondary buttons, you choose three that will open the lock (and can be pressed in any particular order). So, not only do you have to choose the correct master button, but 3 secondary buttons as well. The master control that you choose stays depressed because of a lever, but each secondary button is spring-loaded so it pushes back out when you release it. The interior of the lock (the guts) is made up of springs, neodymium magnets, steel rods, and blocks of wood (Which really should not matter because it has nothing to do with the math problem). So essentially you are choose 1 out of 3 and 3 out of 11 at the same time. So my question is how do i figure out how many differentpossibilities are there in this lock? for example, A, 1, 2, 3 or C, 4, 9, 11.
Is there an equation for this problem, or do I have to sit down and figure it out the long way?