# Math Help - How do you calculate the amount of possible solutions to this two-part lock?

1. ## How do you calculate the amount of possible solutions to this two-part lock?

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?

2. ## Re: How do you calculate the amount of possible solutions to this two-part lock?

Originally Posted by davidbenjamindix
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? <--- that would be a very long way
1. You have 3 possibilities to choose one master button.

2. If it is allowed to push the same sec. button multiple times and if it is allowed to push the sec. button in random order (for instance 5, 5, 8 or 9, 2, 6) then you have $11^3 = 1331$ possibilities to push 3 sec. buttons.

3. The max. number of pushing 4 buttons is therefore 3993.

3. ## Re: How do you calculate the amount of possible solutions to this two-part lock?

Woodworker wants 1 out of 3 master buttons and 3 out of 11 secondary buttons to open lock.

Possibilities= 3* 11C3 = 3* 165 =495