Question

A drawer contains n white and n 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?

Answer 1

2n*(2n-1)

Explanation:

The fundamental rule of counting states that if we want to make an arrangement a1, a2, ..., an of n elements and a1 has k1 ways of being selected, a2 has k2 ways of being selected , …, an has kn ways of being selected, then there are

k1*k2*...*kn different possible arrangements.

In this case we have an arrangement of 2 elements ( 2 socks).

The first sock can be selected in n+n=2n ways. Since there are no replacement, the second sock can be selected in 2n-1 ways.

By the fundamental rule of counting there are 2n*(2n-1) ways of selecting the 2 socks.