1. **State the problem:** Airreen bought 5 packs of nasi lemak costing 15 in total. She has 3 notes of 10, 5 notes of 5, and 5 notes of 1. She picks two banknotes at random one after the other. Find the probability she pays exactly 15. 2. **Understand the problem:** We want the probability that the sum of the two chosen notes equals 15. 3. **Total notes:** $3 + 5 + 5 = 13$ notes. 4. **Total ways to pick 2 notes without replacement:** $$\binom{13}{2} = \frac{13 \times 12}{2} = 78$$ 5. **Possible pairs that sum to 15:** - 10 + 5 = 15 - 5 + 10 = 15 (same as above, order doesn't matter) - 10 + 10 = 20 (too high) - 5 + 5 = 10 (too low) - 10 + 1 = 11 (too low) - 5 + 1 = 6 (too low) - 1 + 1 = 2 (too low) Only pairs of one 10 and one 5 sum to 15. 6. **Count pairs of one 10 and one 5:** - Number of 10 notes = 3 - Number of 5 notes = 5 - Number of such pairs = $3 \times 5 = 15$ 7. **Calculate probability:** $$P = \frac{\text{favorable pairs}}{\text{total pairs}} = \frac{15}{78} = \frac{5}{26}$$ **Final answer:** The probability that she pays exactly 15 is $\boxed{\frac{5}{26}}$.