Therefore, the total number of distinct sundaes is \(\boxed{280}\).
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- \binom{5}{3} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \quad \text{(since } \binom{n}{k} = \binom{n}{n-k} \text{)}
- Total combinations:
- \times 10 = 280
- Question:** A virtual museum has 12 digitized manuscripts, and a curator wants to feature 5 in a weekly digital exhibit. If two specific manuscripts (a solution to an ancient equation and a pivotal scientific letter) must both be included, how many valid selections are possible?
- Solution:** Since two specific manuscripts must be included, we only need to choose the remaining 3 from the other 10 manuscripts.
- The number of ways to choose 3 from 10 is:
