Respuesta :
"different groups" usually means a combination.
[tex] \bf _nC_r=\cfrac{n!}{r!(n-r)!}~\hspace{5em}
\begin{cases}
n=15\\
r=3
\end{cases}\implies _{15}C_3=\cfrac{15!}{3!(15-3)!}
\\\\\\
_{15}C_3=\cfrac{15!}{3!12!}\implies _{15}C_3=\cfrac{15\cdot 14\cdot 13\cdot \underline{12!}}{3!\underline{12!}}\implies _{15}C_3=\cfrac{15\cdot 14\cdot 13}{3!}
\\\\\\
_{15}C_3=\cfrac{15\cdot 14\cdot 13}{3\cdot 2\cdot 1}\implies _{15}C_3=455 [/tex]
I'd also like to point out, most scientific calculator has an [ ₙCᵣ ] button for Combinations as well as [ ₙPᵣ ] for Permutations.
