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1. There are \({7 \choose 5}\) numbers. We simply choose five of the seven digits and once chosen put them in increasing order.

2. This requires stars and bars. Use a star to represent each of the 5 digits in the number, and use their position relative to the bars to say what numeral fills that spot. So we will have 5 stars and 6 bars, giving \({11 \choose 6}\) numbers.