3 inch stack connection

[jjangula]

Basement remodel and adding a kitchenette and washer/dryer combo. It is for the inlaws (partially disabled). Anyway, i have the 3 inch main stack right where sink will go, and the washer plumbing is approx 4 feet away. Can i do a 3 inch to double 2 inch wye to connect both? The drawing is clearly not to scale, and both would have a trap. I can add I vent if needed on the washer side.