Stoopid math fun!

[juncmodule]

Okay, I am developing a form of music composition based on Serialism. It is geared toward MIDI and electronic musicians. I have become stuck in an extremely stoopid and frustrating place.

I am pretty sure the answer to problem 1 is 72.
12x12=144, to avoid duplicates divide by 2 = 72
Since I'm not positive about the answer to problem one that leaves me screwed on problem two. Didn't I learn this stuff in the 3rd grade or something? Why don't I remember this stuff....!? ::)


Here it is:

Serialism

Problem 1:
I am looking for the total possible combinations of 12 notes in a 12 note pattern.

Ex.:

1-2-3-4-5-6-7-8-9-10-11-12

How many ways can these numbers can be reordered without repeating them?

Problem 2:
Part 1--
I am looking for the total possible combinations of two digits from a base of 12 digits.

Ex.:

1-2
3-4
5-6
1-3
etc.

Part 2?
The same as above but with three digits.

1-2-3
3-5-7
1-6-12
etc.

I am not only looking for the solution to this problem but, how it is solved.

THANKS!
-junc

[jelleghys]

Problem 1:
I am looking for the total possible combinations of 12 notes in a 12 note pattern.

12 x 11 x ... x 1 (or a shorter notation = 12! )
On the first spot you have 12 different choises (12), on the 2nd spot you have only 11 choises left (x11), 3rd spot, 10 choises (x10), ...

Problem 2:
Part 1--
I am looking for the total possible combinations of two digits from a base of 12 digits

(12 choises possible, 12 choises possible)
12 x 12 = 144

Part 2—
The same as above but with three digits.

(12 choises possible, 12 choises possible, 12 choises possible)
12 x 12 x 12

[juncmodule]

THANK YOU! ;D