# Math formula needed

1. May 6, 2004

### Greister

Hi,

I was wondering if anyone can help me out here....

I have a series of numbers 1 to 16,
What I would like to know is the formula to finding out how many different sequences I can make with them.

For Example:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 would be one sequence
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1 would be another sequence

I thought that if I multiplied 16 by itself, 16 times this would give me the number of sequences I looking for but the answer I got was
18446744073709551616....This cant be right...right?

Anyway thanks for the help if any given.

2. May 6, 2004

### NateTG

How many different numbers can you put into the first slot?

after you've picked the first number, how many different numbers are left to put into the second slot?

after you've picked the third?
and so on?

3. May 6, 2004

### Greister

It's like the lotto...I have 16 balls numbered 1-16, there are no duplicate numers.
and there are 16 slots that the balls fall into...all the balls are used filling up the 16 slots.

I need the total number of UNIQUE sequences they can be made into.

Q1 = 16
Q2 = 15
Q3 = 14 ...and so on

4. May 6, 2004

### fourier jr

There are:
16 possibilities for the 1st slot,
15 possibilities for the 2nd slot since 1 number is used up,
14 possibilities for the 3rd slot since 2 numbers are used up,
..... etc

so that makes 16! = 16*15*14*13* .... *3*2*1 = 20,922,789,888,000 (not 18,446,744,073,709,551,616)

right? I never liked discrete so I might be wrong. (I'm probably wrong & confused everybody )

Last edited: May 6, 2004
5. May 6, 2004

### Greister

Sounds right, Its just when I was in school for programming there was an equation to get exactly what Im looking for, which for the life of me I cant find in my past notes. It was some kind of probability equation...

Sorry for my ignorance....from reading the posts on these forums I think Im way out of my league here...hehe

6. May 7, 2004

### humanino

do not play lotto... (^_^)

7. May 7, 2004

### NateTG

There is no general closed form for factorial. It's denoted with an exclamation mark i.e. the number you're looking for can be written as 16!. If you only want approximations, you can look into stirling's approximation and the error function.