Solve 5^x-2 = 200. round your answer to the nearest hundredth.

a) 2n(2n-1)

b) 2n(n-1)

c)

Step-by-step explanation:

There are in total n + n = 2n socks.

(a) How many ways are there to select the two socks?

The first sock can be selected in 2n different ways. The second sock can be selected in 2n-1 ways.

Since the order in which the socks are selected does not matter, by the Fundamental Principle of Counting there are

2n(2n-1)  

different ways of selecting two socks.

(b) How many ways of selecting the socks result in two socks of the same color being chosen?

There are n(n-1) different ways of selecting two white socks and n(n-1) ways of selecting two black socks, so there are

n(n-1) + n(n-1) = 2n(n-1)  

ways of selecting two socks of the same color.

(c)What is the probability that a randomly chosen pair of socks are the same color?

If every way of selecting the two socks is equally likely, the probability is