A bag contains $4$ White shirts, $4$ Black shirts and $6$ Pink shirts. If two shirts are drawn randomly, what is the probability that at most one shirt is white?

Total number of shirts $=4+4+6=14$.
Number of ways to draw $2$ shirts out of $14$:

$$\text{Total Outcomes}=\left(\genfrac{}{}{0ex}{}{14}{2}\right)=\frac{14\times 13}{2}=91$$

"At most one white shirt" means we can draw either $0$ white shirts or $1$ white shirt. Alternatively, we can subtract the probability of drawing exactly $2$ white shirts from $1$:

$$\text{Ways to draw 2 White shirts}=\left(\genfrac{}{}{0ex}{}{4}{2}\right)=\frac{4\times 3}{2}=6$$

$$\text{Probability of 2 White shirts}=\frac{6}{91}$$

$$\text{Probability of at most 1 White shirt}=1-\frac{6}{91}=\frac{85}{91}$$