Question

Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
A. 7/26
B. 1/7
C. 14/33
D. 1/49

Answer 1

Answer:

P=2/7.

Step-by-step explanation:

We know that  sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot.

Two white socks, four brown socks, and two black socks = 8 socks.

We calculate the number of possible combinations:

$C^8_2=\frac{8!}{2!(8-2)!}=28$

We calculate the number of favorable combinations:

$C_1^2\cdot C^4_1=2\cdot 4=8$

Therefore, the probability is

P=8/28

P=2/7.