Salmon run: friend didn't get specifically splattershot (weapon) for 3 games in a row.

[penny.spl]

Me and my friends play a game called splatoon and there's something called Salmon run and one of my friends claimed he didn't get specifically splattershot (weapon) for 3 games in a row. We wanted to know the probability of this but we all seem to get different answers so I came for help. For context each game has 3 waves and there is four weapons the game can give you on the first wave. but you can't get the same weapon twice so on the second wave there's only 3 weapons the game can give you and the last wave only 2.So you are bound to not play one specific weapon each gane. If there's any other information or clarification you'd need to solve this let me know!

 

[MaxWong]

From your description, there are exactly [imath]4 \times 3 \times 2[/imath] different combinations of weapons you can get. But in order to not get splattershot, there are only 3 different choices on the first wave, 2 choices on the second wave, and 1 choice on the last. Therefore, assuming the each weapon is equally likely to be chosen, the probability is [imath]\dfrac{3 \times 2 \times 1}{4\times 3 \times 2} = \dfrac14[/imath].