Assuming the triplets are identical and cannot be told apart, how many distinguishable photographs can be taken of a family of 5, if they stand in a single row and there is one set of triplets?
A) 60
B) 40
C) 20
D) 120

Question

Quizplus · Accepted Answer

There are 5 people in total, but since the triplets are identical and cannot be discerned from each other, we can treat them as one unit. Therefore, there are really only 3 units to arrange (the triplets, plus the other two individuals). The number of ways to arrange 3 units is 3!, or 6. However, we must also consider the fact that the two non-triplet individuals can switch places, so we need to divide by 2 for each of the 6 arrangements, giving us a total of 3 arrangements. Finally, we can arrange the triplets within their unit in 3! ways, giving us a total of 3x3! = 18 arrangements. However, we must also consider the fact that the two individuals on the ends of the row can switch places, giving us 2 more arrangements, for a total of 20.

Assuming the Triplets Are Identical and Cannot Be Told Apart