There are a total of 6 lettered buttons on the controller. Since the special moves require two buttons pressed at the same time, the order does not matter. We therefore get
[tex]\begin{gathered} \binom{6}{2}=\frac{6!}{2!(6-2)!} \\ \binom{6}{2}=\frac{6\cdot5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}1}{(2\operatorname{\cdot}1)(4!)} \\ \binom{6}{2}=\frac{720}{2(4\cdot3\operatorname{\cdot}2\operatorname{\cdot}1)} \\ \binom{6}{2}=\frac{720}{2(24)} \\ \binom{6}{2}=\frac{720}{48} \\ \binom{6}{2}=15 \end{gathered}[/tex]
Therefore, there are a total of 15 possible combinations.
