Easy gun, you will need to travel to vault 81. To enter vault 81 you will need to pay the overseer 3 fusion cores. Not to bad and worth the cost for this weapon! Once inside the vault, head down the elevator, make a right and the first room on the right will be titled the "depot" inside is a vendor here name is "Alexis Combes" talk to her and you can buy the gun from her, gun is around 3000 caps. All details below !

Short barell combat rifle with scope, shoots an additional projectile

Heres the location of vault 81
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Heres a video to follow along to if youd like