A drawer contains 2 brown and 3 gray socks. THe socks are taken out of the drawer one at a time. WHat is the probability that the fourth sock removed is gray? Express your answer as a common fraction.

Can anyone explain this to me? Thanks!!

there are 10 ways to arrange the 5 socks

5!/2!3!) = 10

lets list them in an organized way:
BBGGG
BGBGG
BGGBG
BGGGB

GBBGG
GBGBG
GBGGB

GGBBG
GGBGB
GGGBB
Looks like the G is in the 4th spot 6 times
so the prob is 6/10 = 3/5

3/5

A printer can print 10 pages of text per minute or 4 pages of graphics per minute. How many minutes will it take to print 31 pages of text and 7 pages of graphics? Express as a mixed numer.

Sure! To find the probability that the fourth sock removed is gray, we need to understand the total number of possible outcomes and the number of favorable outcomes.

Let's first determine the total number of possible outcomes. When selecting the socks one at a time, on each draw, the number of available socks decreases. So, for the first draw, there are a total of 5 socks in the drawer. For the second draw, there are only 4 socks left, and so on.

To calculate the total number of possible outcomes, we need to multiply the number of socks in the drawer for each draw:

Total number of outcomes = 5 (for the first draw) * 4 (for the second draw) * 3 (for the third draw) * 2 (for the fourth draw) = 120

Next, we determine the number of favorable outcomes. We want the fourth sock removed to be gray, so we need to consider the number of gray socks remaining in the drawer at the fourth draw. Since there are initially 3 gray socks in the drawer, and one sock is removed on each draw, there will be 1 gray sock left in the drawer for the fourth draw.

The number of favorable outcomes is, therefore, the number of ways to choose the 1 remaining gray sock out of the total 120 possible outcomes.

Number of favorable outcomes = 1

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of outcomes = 1 / 120

Therefore, the probability that the fourth sock removed is gray is 1/120.