Step 1: {Digit Classification}
The number comprises the digits \( 2, 2, 3, 3, 5, 5, 8, 8, 8 \). This set includes 4 odd digits (\( 3, 3, 5, 5 \)) and 5 even digits (\( 2, 2, 8, 8, 8 \)).
Step 2: {Arranging Odd Digits}
The odd digits must be placed in the even-numbered positions of the nine-digit number. With 4 even positions available, the number of permutations for placing the odd digits is calculated as: \[ \frac{4!}{2!2!} = 6. \]
Step 3: {Arranging Even Digits}
The 5 remaining odd positions are to be filled by the even digits. The number of ways to arrange the even digits in these positions is: \[ \frac{5!}{2!3!} = 60. \] Consequently, the total number of possible arrangements is \( 6 \times 60 = 60 \), corresponding to option (C).