1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution the answer for no adjoining _W_W_W_W_W_ for 3 red balls, there are 6 positions so ## 6C_3 = 20## i'm curious, on other way to find arrangement? for adjoining = all arrangement - adjoining all arrangement = 3 red can get to any positions _ _ _ _ _ _ _ _ while white at the rest i'm curious on other way to find arrangement? so ## 8C_3 = 56 ## adjoining = 56 - 20 = 36 i'm curious on how to find adjoining directly without ' all arrangement - adjoining ' ?