Math Formula Needed to Calculate Sequences

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Discussion Overview

The discussion revolves around finding a mathematical formula to calculate the number of unique sequences that can be formed using the numbers 1 to 16. Participants explore the concept of permutations and factorials, addressing the problem from various angles, including programming perspectives and probability equations.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant questions the method of calculating sequences by suggesting multiplying 16 by itself 16 times, leading to a very large number.
  • Another participant prompts a breakdown of the selection process for each slot, indicating that the number of choices decreases as numbers are used.
  • A comparison is made to a lottery scenario, emphasizing that all numbers are unique and used to fill slots.
  • It is noted that the total number of unique sequences can be calculated as 16! (16 factorial), which equals 20,922,789,888,000, correcting the earlier large number presented.
  • One participant expresses uncertainty about their understanding of discrete mathematics and the factorial concept.
  • Another participant mentions a probability equation from their programming studies that could relate to the problem but cannot recall it.
  • A suggestion is made to consider Stirling's approximation for approximating factorials, although it is noted that there is no general closed form for factorials.

Areas of Agreement / Disagreement

Participants generally agree on the factorial approach to calculating the number of unique sequences, but there is uncertainty about the exact formula and its derivation. Some participants express confusion about the concepts involved.

Contextual Notes

There are references to programming perspectives and approximations, indicating a potential gap in understanding the mathematical foundations of permutations and factorials. The discussion includes varying levels of familiarity with discrete mathematics.

Who May Find This Useful

This discussion may be useful for individuals interested in combinatorial mathematics, programming applications of permutations, or those seeking clarification on factorial calculations.

Greister
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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 can't be right...right?

Anyway thanks for the help if any given.
 
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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?
 
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.

The answer to your question above is

Q1 = 16
Q2 = 15
Q3 = 14 ...and so on
 
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? :confused: I never liked discrete so I might be wrong. (I'm probably wrong & confused everybody :frown: )
 
Last edited:
Sounds right, Its just when I was in school for programming there was an equation to get exactly what I am looking for, which for the life of me I can't 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 I am way out of my league here...hehe
 
do not play lotto... (^_^)
 
Greister said:
Sounds right, Its just when I was in school for programming there was an equation to get exactly what I am looking for, which for the life of me I can't 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 I am way out of my league here...hehe

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.
 

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