1. **State the problem:** We need to find which number among 45, 60, 91, 105, and 330 is the product of exactly three distinct prime numbers. 2. **Recall the concept:** A product of three distinct prime numbers means the number can be expressed as $$p \times q \times r$$ where $$p, q, r$$ are prime numbers and all different. 3. **Factorize each number into primes:** - 45: $$45 = 3^2 \times 5$$ (only two distinct primes: 3 and 5) - 60: $$60 = 2^2 \times 3 \times 5$$ (three distinct primes: 2, 3, 5) - 91: $$91 = 7 \times 13$$ (two distinct primes: 7 and 13) - 105: $$105 = 3 \times 5 \times 7$$ (three distinct primes: 3, 5, 7) - 330: $$330 = 2 \times 3 \times 5 \times 11$$ (four distinct primes: 2, 3, 5, 11) 4. **Check which have exactly three distinct primes:** - 60 has 2, 3, 5 (three distinct primes) - 105 has 3, 5, 7 (three distinct primes) 5. **Conclusion:** Both 60 and 105 are products of three distinct prime numbers. However, since the question asks for the balloon that is the product of three distinct primes, and 60 includes a squared prime (2 squared), it still counts as three distinct primes. Therefore, the balloons with numbers 60 and 105 fit the condition, but 105 is the product of exactly three distinct primes without any repeated prime factors. **Final answer:** The balloon with number **105** is the product of three distinct prime numbers.