To solve this problem, we need to calculate the number of permutations of the five individuals under the constraint that Esi (E) must always stand immediately behind Becky (B).

Step-by-step solution:

1. Treat Becky and Esi as a single block:

   • Since Esi must stand immediately behind Becky, we can consider them as a single "unit" or block. This reduces the number of entities to arrange from 5 to 4: {BE (the block), Anneliese (A), Carlo (C), Dan (D)}.

2. Permute the 4 entities:

   • The number of ways to arrange 4 entities is $4! = 24$.

3. Arrange Esi and Becky within their block:

   • Within the block "BE," Becky must be first, and Esi must be immediately behind her. This arrangement is fixed, so there is only 1 way to arrange them within the block.

4. Total permutations:

   • Multiply the number of ways to arrange the blocks by the number of ways to arrange Becky and Esi within their block: $4! \times 1 = 24$

Final Answer:

The total number of permutations is 24.

Correct option: b. 24

Do you want additional details or further clarification? Here are related questions to consider:

1. What if Esi could stand immediately in front of Becky instead?
2. How many permutations are possible if Esi must stand anywhere near Becky (not just behind)?
3. How does the calculation change if there are more people in line?
4. What if the order of the line was completely unrestricted?
5. How many ways can the group line up if Becky and Esi refuse to stand next to each other?

Tip: When solving permutation problems with constraints, simplify by grouping dependent items into blocks first!