Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?
- A. \frac{1}{81}
- B. \frac{1}{72}
- C. \frac{1}{18}
- D. \frac{1}{36} ✓
Correct Answer: D. \frac{1}{36}
Explanation
The total number of ways to pick 2 distinct numbers from 9 is {}^9C_2 = 36. For the product to end in 1, the unit digits of the numbers must multiply to a number ending in 1. Among the digits 1 to 9, the pairs are (1,1), (3,7), (9,9). Since the numbers must be distinct, the only valid pair is \{3, 7\}. There is only 1 such pair. Thus, the probability is \frac{1}{36}.
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