In a group of four people, how many social relationships link the members?A.fiveB.threeC.sixD.four

To determine the number of social relationships in a group of four people, we can think of each relationship as a connection between two people. This is a classic problem in combinatorics, where we need to find the number of ways to choose 2 people out of 4 to form a relationship.

The formula for combinations is given by:

$\binom{n}{k} = \frac{n!}{k!(n-k)!}$

where $n$ is the total number of people, and $k$ is the number of people in each group (in this case, 2).

For our problem:

• $n = 4$ (the total number of people)
• $k = 2$ (since a relationship involves 2 people)

Plugging these values into the formula, we get:

$\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4!}{2! \cdot 2!}$

Calculating the factorials, we have:

$4! = 4 \times 3 \times 2 \times 1 = 24$ $2! = 2 \times 1 = 2$

So,

$\binom{4}{2} = \frac{24}{2 \times 2} = \frac{24}{4} = 6$

Therefore, the number of social relationships linking the members of the group is 6.

The correct answer is: C. six