Final answer:
The question can be solved using the concept of permutations in combinatorics. There are 6 different arrangements for Luke, Aiden, and Brogan to stand side by side for their photo, determined by the calculation 3 x 2 x 1.
Step-by-step explanation:
The question posed is regarding the number of different ways Luke, Aiden, and Brogan can be arranged for their photo when standing side by side. This scenario is a permutation problem, which is a concept from combinatorics within mathematics that deals with the arrangement of objects.
To find the total number of unique arrangements for the three boys, we can perform a straightforward calculation. Each position can be filled by any of the three, but once one has been placed, the next position can only be filled by one of the remaining two, and the last position is filled by the last remaining boy. So, the calculation process involves multiplying these possibilities together:
- Choose a boy for the first position: 3 options (Luke, Aiden, or Brogan).
- Choose a boy for the second position: 2 options (the remaining boys).
- The third position will be filled by the last remaining boy: 1 option.
Multiplying these numbers together, the total number of arrangements is 3 x 2 x 1, which equals 6 different ways.
To summarize, there are 6 different arrangements in which Luke, Aiden, and Brogan can stand side by side for their picture.