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DinhNgocHien · Answer 1 · 2023-10-21T16:41:27+0000

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

$\begin{gathered} \binom{6}{2}=(6!)/(2!(6-2)!) \\ \binom{6}{2}=\frac{6\cdot5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}1}{(2\operatorname{\cdot}1)(4!)} \\ \binom{6}{2}=\frac{720}{2(4\cdot3\operatorname{\cdot}2\operatorname{\cdot}1)} \\ \binom{6}{2}=(720)/(2(24)) \\ \binom{6}{2}=(720)/(48) \\ \binom{6}{2}=15 \end{gathered}$

Therefore, there are a total of 15 possible combinations.

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