That's not true. If [tex]n\mathrm Cr[/tex] and [tex]n\mathrm Pr[/tex] are defined as
[tex]n\mathrm Cr=\dfrac{n!}{r!(n-r)!}[/tex]
[tex]n\mathrm Pr=\dfrac{n!}{(n-r)!}[/tex]
then
[tex]\dfrac{n\mathrm Cr}{n\mathrm Pr}=\dfrac{\frac{n!}{r!(n-r)!}}{\frac{n!}{(n-r)!}}=\dfrac1{r!}[/tex]
