Step 1: Understanding the Concept:
Calculate the number of odd days between the two dates.
Step 2: Detailed Explanation:
1. From 17th Dec 2002 to 17th Dec 2003 = 1 odd day (Normal year).
2. From 17th Dec 2003 to 17th Dec 2004 = 2 odd days (2004 is a leap year).
3. Total odd days for years = $1 + 2 = 3$.
Step 3: Calculation:
1. Days from 17th Dec 2004 to 22nd Dec 2004 = 5 days.
2. Total odd days = $3 + 5 = 8$ odd days.
3. $8 \div 7$ leaves a remainder of 1.
4. Saturday + 1 day = Sunday? Let's re-calculate.
Correction: 2004 is a leap year, and February 2004 falls between the two dates.
Dec 17, 2002 to Dec 17, 2003 (+1) $\to$ Sunday.
Dec 17, 2003 to Dec 17, 2004 (+2) $\to$ Tuesday.
Dec 17, 2004 to Dec 22, 2004 (+5 days) $\to$ Tuesday + 5 = Wednesday.
Step 4: Final Answer:
The day was Wednesday. Thus, the correct option is (c).