Question

A sock drawer has 8 blue socks and 6 black socks. If I randomly select two socks, one at a time, what is the probability I will first get a blue sock and then, without replacing it, a black sock?

A. 24/91 B. 2/7 C. 6/81 D. 4/13

Answer 1

a. 24/91
Step-by-step explanation:

Calculate first the total number of permutation possible.

You select two socks so that will be:

14⋅13=182

Now you must first select a blue sock then a black sock:

You can only pick 8 possible blue socks
You can only pick 6 possible black socks

which means that this permutation (blue→black) have 8⋅6=48 possibilities for each different blue and black sock.

express in fraction:

48182=2491