The difference between 3.5 and 4 is substantial. Here is what 4 says
To find the number of combinations in which four friends (A, B, C, and D) can stand in line such that A and C are not next to each other, we can use the following approach:
Total Combinations: First, calculate the total number of ways in which four people can be arranged in a line. This can be calculated by (4!) (4 factorial), since there are 4 slots to fill, each choice reducing the number of available choices by one for the next slot. [ 4! = 4 \times 3 \times 2 \times 1 = 24 ]
Unwanted Combinations (Where A and C are next to each other):
Consider A and C as a single unit. This effectively reduces the number of units to arrange from 4 to 3 (the AC unit, B, and D).
These three units can be arranged in (3!) ways: [ 3! = 3 \times 2 \times 1 = 6 ]
However, within the AC unit, A and C can switch places. So, there are 2 ways to arrange A and C within their unit.
Therefore, the total number of arrangements where A and C are next to each other is: [ 3! \times 2 = 6 \times 2 = 12 ]
Subtracting Unwanted Combinations: Subtract the number of unwanted combinations (where A and C are next to each other) from the total number of combinations: [ 24 - 12 = 12 ]
Thus, there are 12 combinations where A and C are not next to each other.