# Time to test all combinations

1. Mar 10, 2014

### SteveH66

I am not sure if this is the right sub-forum to post this question in or not, if not I appologize for posting in the wrong place - it looked like the most likely forum to be the correct one.

In a sci-fi book I was reading, the author talked about an 'artificial symbiote' being created by 15 molecular pieces aligned correctly, which had been stolen from the villians. He said the possible combinations were in the millions, and that if you tested one combination per second, it would take over 4,000 years. This has been nagging at me for quite a while, I did what I thought was the proper calculation to find this out, to check his figures and I come up with much different numbers. So I was wondering if someone could tell me if I am not calculating this correctly.

First, I decided you would have to calculate 15 to the 15th power, 15^15, to get the number of possible combinations. When I do this, I get over 437 Quadrillion possible combinations 437,893,890,380,859,000. Next I calculated the number of seconds in a year, I got 31,536,000. Then I divided the number of calculations by the number of seconds in a year. Instead of 4,000 I got 13,885,524,174.94

13 billion is a lot different than 4,000 so I am puzzled. Am I calculating this wrong, or is the author? Thanks for any light you can shine on this problem for me.

2. Mar 10, 2014

### mathman

The description is a little vague.
One possible interpretation. 15 items to be placed in proper order. The number of possibilities is 15! = 1307674368000. This leads to 41000 years.

3. Mar 10, 2014

### h6ss

Do we know how the molecular pieces are chosen to be aligned?

If they must be placed in a specific order, then the number of possibilities is 15! instead of 15^15.

4. Mar 10, 2014

### SteveH66

I don't know a lot about advanced mathematics, so I don't know what 15! is, but yes H6ss, the molecular pieces of the compound(?) must be placed in a specific order to work. If any of the 15 are out of order, the compound will not function. So it sounds like 15! would be correct as you stated it. Where would I go to find out more about 15! ? What is the name for this type of calculation? I find the math behind things like this very interesting. Thanks for the help mathman and h6ss.

5. Mar 10, 2014

### h6ss

n! is the factorial of n, which is the product of all positive integers less than or equal to n.

For example, 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

It is used notably in combinatorics: there are n! different ways of arranging n distinct objects into a sequence.