Cuphead is a 2D shooter game in which a player can permanently acquire up to [edit: six] different Shots (i.e., weapons) and up to six different Charms (i.e., perks or buffs).
However, a player can only equip two Shots (one active, one reserve) and one Charm at a time. Note that a player cannot have the same the Shot be both active and reserve.
How many two-Shot, one-Charm [edit: permutations] are possible?
FYI I once attended a few lectures of an undergrad Probability course. My understanding is that…
[edit: 6] possible active Shots * [edit: 5] possible reserve Shots * 6 possible Charms = [edit: 180] possible [permutations]
Is this calculation correct? Also, assuming that a second player can have any identical two-Shot, one-Charm setup as the first player, would the possible combinations of setups for two players then be…
[edit: 180] possible setups for Player 1 * [edit: 180] possible setups for Player 2 = [edit: 32,400] possible setups for the pair
Best Answer
It depends on whether or not you distinguish between primary and secondary weapons. For instance, if you don't care which is primary and which is secondary then there are $\binom{5}{2}=10$ ways to choose any two weapons, but if you care about which is primary and which is secondary, then there are $5 \cdot 4=20$ ways to choose the 2 weapons. Your calculation uses the latter and thus distinguishes two hands if the primary and secondary weapons are swapped, so if this is what you intended then the calculation is correct.