a drawer contains white and black socks. each white sock has a unique design, and each black sock has a unique design. two socks are selected at random from the drawer. every way of selecting the two socks is equally likely, and the order in which the socks are selected does not matter. source: aduni, modified by sandy irani. (a) how many ways are there to select the two socks? (b) how many ways of selecting the socks result in two socks of the same color being chosen? (c) what is the probability that a randomly chosen pair of socks are the same color? simplify your final expression as much as possible so that it does not include any expressions of the form .

The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is.
P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.

Let the number of white and black socks be 'n' each.

Then, total n + n = 2n socks.

(a) There are numerous ways to choose the two socks:

There are 2n methods to choose the first sock. There are 2n-1 different ways to choose the second sock.

Because it is irrelevant which socks are chosen first, according to the Fundamental Principle of Counting, there are

2n(2n-1)

Alternative approaches to choosing two socks.

(b) Regardless matter how the socks are picked, two with same color are always chosen:

There are n(n-1) distinct methods to choose two white socks plus n(n-1) different ways to choose two black socks.

n(n-1) + n(n-1)

= 2n (n-1)

Methods for choosing two socks with the same hue.

(c) The likelihood that two socks picked at random have the same color:

If there is an equal chance of choosing any two socks, the probability is:

= 2n(n - 1)/2n(2n - 1)

= (n - 1)/(2n - 1)

The likelihood that two socks picked at random have the same color: (n - 1)/(2n - 1).

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