# Math Help - Tracing numbers - Induction needed ?

1. ## Tracing numbers - Induction needed ?

Hi !

is it true that any set of tracing numbers (1, 2, 3, 4...) can be divided (no remainder) by the factorial n!, whereas "n" is the numbers of integers in the group ?

example: 3, 4, 5, 6 (n = 4)
can be devided by: 4! = 24.

and how can i prove it...?

thanx a lot !

2. Originally Posted by dudinka
Hi !

is it true that any set of tracing numbers (1, 2, 3, 4...) can be divided (no remainder) by the factorial n!, whereas "n" is the numbers of integers in the group ?

example: 3, 4, 5, 6 (n = 4)
can be devided by: 4! = 24.

and how can i prove it...?

thanx a lot !
If I understand you correctly you want to prove that $(k-n+1) \cdot (k-n+2) \cdot \dots \cdot k$ (n factors, starting at k-n+1)is always divisible by $n!$, regardless what k and n are.
This is correct, the quotient is $\binom{k}{n}$ which is always an integer.

3. ## thank you

thanks a lot.