Non-Adjacent Ones

Arrange the 6 zeros first, creating gaps to place the ones.

Placing 6 zeros creates 7 gaps; choose 4 gaps for the ones.

1. 1. Set up gap method

   Place the 6 zeros in a row, creating 7 gaps (including ends) where ones can go, at most one 1 per gap to avoid adjacency.

2. 2. Choose gaps

   Choose 4 of these 7 gaps for the ones: $\left(\genfrac{}{}{0ex}{}{7}{4}\right)$.

   $$\left(\genfrac{}{}{0ex}{}{7}{4}\right)=35$$

Answer: 35