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Explanation:

Let O and E represent odd and even digits respectively.

∴ S can have digits of the form:

O _ O _ E or O _ E _ O or E _ O _ O 

Case 1: O _ O _ E
The first digit can be chosen in 3 ways out of 1, 3 and 5
The third can be chosen in 2 ways.
The fifth digit can be chosen in 2 ways after which the second and fourth digits can be chosen in 2 ways.
 ∴ There are 3 × 2 × 2 × 2 = 24 ways in which this number can be written.
12 out of these ways will have 2 in the rightmost position and 12 will have 4 in the rightmost position.
∴ The sum of the rightmost digits in Case 1 = (12 × 2) + (12 × 4) = 72 

Case 2: O _ E _ O
This number can again be written in 24 ways.
8 out of these ways will have 1 in the rightmost position, 8 will have 3 in the rightmost position and 8 will have 5 in the rightmost position. 
Thus the sum of the rightmost digits in Case 2 = (8 × 1) + (8 × 3) + (8 × 5) = 72 

Case 3: E _ O _ O
This number can also be written in 24 ways.
As in Case 2, 8 out of these ways will have 1 in the rightmost position, 8 will have 3 in the rightmost position and 8 will have 5 in the rightmost position.
∴ The sum of the rightmost digits in Case 3 = (8 × 1) + (8 × 3) + (8 × 5) = 72 

∴ The sum of the digits in the rightmost position of the numbers in S = 72 + 72 + 72 = 216

Hence, option (b).

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