A box has 6 black, 4 red, 2 white and 3 blue shirts. What is probability of picking at least 1 red shirt in 4 shirts that are randomly picked?

Answer: Option C

Choosing 4 shirts means 1^st shirt and 2^nd and then 3^rd and then 4^th shirt
At least 1 red shirt means there can be 1, 2, 3 or 4 red shirts
So, Probability of choosing red = 1 - Probability of not choosing red
If we remove red shirts, then 15 - 4 red shirts = 11 shirts remain.
We have to choose 4 out of these 11
So Probability of choosing 4 shirts which are not red
$$\begin{array}{rl}& =\frac{11}{15}\times \frac{10}{14}\times \frac{9}{13}\times \frac{8}{12}\\ & =\frac{22}{91}\end{array}$$
∴ Probability of picking at least 1 red shirt
$$\begin{array}{rl}& =1-\frac{22}{91}\\ & =\frac{69}{91}\end{array}$$