A box has 6 black, 4 red, 2 white and 3 blue shirts. What is the probability that 2 red shirts and 1 blue shirt get chosen during a random selection of 3 shirts from the box?

Answer: Option A

We want 2 red and 1 blue shirt
There are 4 red shirts and 3 blue shirts
Total = 15 shirts
You can choose blue shirt 1^st, then red shirt
And then red shirt Probability
$$\begin{array}{rl}& =\frac{3}{15}\times \frac{4}{14}\times \frac{3}{13}\\ & =\frac{6}{455}\end{array}$$
Or you can choose red shirt 1^st, then red shirt and then blue shirt
Or you can choose red shirt 1^st, then blue shirt and then red shirt
For all 3 the probability remains same = $$\frac{6}{455}$$
We need to add these 3 probabilities to get total probability
∴ Total probability
$$\begin{array}{rl}& =\frac{6}{455}+\frac{6}{455}+\frac{6}{455}\\ & =\frac{18}{455}\end{array}$$