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?

Solution(By Examveda Team)

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
$$\eqalign{ & = \frac{{11}}{{15}} \times \frac{{10}}{{14}} \times \frac{9}{{13}} \times \frac{8}{{12}} \cr & = \frac{{22}}{{91}} \cr} $$
∴ Probability of picking at least 1 red shirt
$$\eqalign{ & = 1 - \frac{{22}}{{91}} \cr & = \frac{{69}}{{91}} \cr} $$