Question

a drawer contains one pair of brown socks and one pair of white socks. the table shows the possible outcomes, for choosing a sock, replacing it, and then choosing another sock. if the first sock is not replaced, how many possible outcomes are there? how many of these outcomes contain a matching pair of socks? counting outcomes

Explanation:

First Question: Number of possible outcomes (without replacement)

Step1: Identify total socks

A pair of brown (2 brown) and a pair of white (2 white), so total \( 2 + 2 = 4 \) socks.

Step2: Calculate permutations (without replacement)

When choosing 2 socks without replacement, the number of ways is \( P(4,2)=\frac{4!}{(4 - 2)!}=4\times3 = 12 \). Alternatively, count the table: Sock 1 has 4 options, Sock 2 has 3 (since no replacement), so \( 4\times3 = 12 \).

Step1: Identify matching pairs

Brown - Brown (b,b) and White - White (w,w).

• For brown: First brown (2 choices), second brown (1 remaining), so \( 2\times1 = 2 \) ways.
• For white: First white (2 choices), second white (1 remaining), so \( 2\times1 = 2 \) ways.

Step2: Total matching pairs

Add them: \( 2 + 2 = 4 \).

Answer:

12

Second Question: Number of matching pairs