there are 4 students sitting to receive their prizes. Alan and Julia wanted to sit together. how many different arrangements of students would there be
To find the number of different arrangements of the students, we need to consider the condition that Alan and Julia should sit together.
Let's consider Alan and Julia as one unit. So, now we have three units: Alan and Julia together, and the other two students (let's call them B and C).
Now, we can arrange these three units (Alan & Julia, B, and C) in 3! = 3 * 2 * 1 = 6 different ways.
However, within the Alan & Julia unit, Alan and Julia can swap positions. Hence, for each of the 6 arrangements, we can have 2 different arrangements of Alan and Julia sitting together.
Therefore, the total number of different arrangements would be 6 * 2 = 12.