Solution:
To find the number of elements in S5, the permutation group on 5 symbols, such that a5 = a2, we need to consider the possible permutations and count the number of elements that satisfy the given condition.

Permutations in S5:
S5 is the permutation group on 5 symbols, which means it consists of all possible permutations of these 5 symbols: {1, 2, 3, 4, 5}. The total number of elements in S5 is given by 5!, which is equal to 5 x 4 x 3 x 2 x 1 = 120.

Finding elements with a5 = a2:
Given that a5 = a2, we can consider the positions of these two elements in a permutation. There are two cases to consider:

Case 1: a5 and a2 are in the same cycle.
In this case, the elements can be arranged in a cycle of length 2, such as (a5 a2), and the remaining 3 elements can be arranged in any order. The number of permutations in this case is given by (2-1)! x (5-2)! = 1 x 3! = 6.

Case 2: a5 and a2 are in different cycles.
In this case, the elements can be arranged in two separate cycles of length 1, such as (a5) and (a2), and the remaining 3 elements can be arranged in any order. The number of permutations in this case is given by (1!) x (1!) x (5-2)! = 1 x 1 x 3! = 6.

Total number of permutations with a5 = a2:
To find the total number of permutations that satisfy the given condition, we need to add the permutations from both cases:
Total permutations = permutations in case 1 + permutations in case 2 = 6 + 6 = 12.

Answer:
The correct answer is not given in the options provided. The actual number of elements in S5, such that a5 = a2, is 12.