Suppose that 4 people sit in 4 chairs in a circle. How many different new seating arrangemens are possible if each person can move 1 chair to the left or right or remain as is and if 1 person must be in each chair?
To solve this problem, we can use the concept of permutations.
If we consider the 4 chairs as fixed positions labeled A, B, C, and D, we can assign each person to one of these chairs.
Start by selecting one person to sit in chair A. We have 4 options for this selection.
Now, for each subsequent person, we have three options: they can either move 1 chair to the left, move 1 chair to the right, or remain in their current seat.
Considering this, we can determine the total number of seating arrangements by multiplying the number of options for each person together.
For the second person, there are 3 options. After the second person has made their choice, the third person will also have 3 options. Finally, the fourth person will have 3 options as well.
So, the total number of seating arrangements is: 4 * 3 * 3 * 3 = 108.
Therefore, there are 108 different seating arrangements possible under the given conditions.