Answer :
To determine the value of "4 things taken 2 at a time," we can calculate the number of combinations. Combinations are given by the formula:
\[ C(n, k) = \frac{n!}{k!(n - k)!} \]
where \( n \) is the total number of items, \( k \) is the number of items to choose, and \( ! \) denotes factorial.
In this problem, \( n = 4 \) and \( k = 2 \). Consequently, we can substitute these values into our formula and carry out the calculation:
\[ C(4, 2) = \frac{4!}{2!(4 - 2)!} \]
Calculating factorials:
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]
\[ 2! = 2 \times 1 = 2 \]
\[ (4 - 2)! = 2! = 2 \]
Substituting these factorials into the combination formula gives us:
\[ C(4, 2) = \frac{24}{2 \times 2} = \frac{24}{4} \]
\[ C(4, 2) = 6 \]
Therefore, the value of "4 things taken 2 at a time" is 6.
