1. **State the problem:** Kannika has 9 counters with numbers: 1, 1, 2, 3, 3, 3, 5, 6, 6. She draws two counters without replacement. We need to find the probability that the sum of the two numbers is less than 5. 2. **Total number of ways to pick 2 counters:** Since order does not matter and no replacement, total combinations are $$\binom{9}{2} = \frac{9 \times 8}{2} = 36$$. 3. **Identify pairs with sum less than 5:** Possible sums less than 5 are 2, 3, or 4. - Sum = 2: (1,1) - Sum = 3: (1,2) and (2,1) - Sum = 4: (1,3), (3,1), (2,2), (3,1) but 2,2 is not possible since only one 2. 4. **Count the favorable pairs:** - (1,1): There are two 1s, so number of pairs is $$\binom{2}{2} = 1$$. - (1,2): Number of 1s = 2, number of 2s = 1, so pairs = $$2 \times 1 = 2$$. - (1,3): Number of 1s = 2, number of 3s = 3, so pairs = $$2 \times 3 = 6$$. - (2,3): Sum is 5, so exclude. - (3,3): Sum is 6, exclude. Total favorable pairs = $$1 + 2 + 6 = 9$$. 5. **Calculate probability:** $$\text{Probability} = \frac{\text{favorable pairs}}{\text{total pairs}} = \frac{9}{36} = \frac{1}{4}$$. **Final answer:** The probability that the sum of the two counters is less than 5 is $$\boxed{\frac{1}{4}}$$.