1. **Problem:** How many different combinations of six numbers can be chosen from the digits 1 to 8 if each digit is chosen only once? 2. **Formula:** The number of combinations of choosing $k$ elements from $n$ distinct elements is given by the binomial coefficient: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. **Calculation:** Here, $n=8$ and $k=6$. $$\binom{8}{6} = \frac{8!}{6!2!}$$ 4. **Simplify factorials:** $$= \frac{8 \times 7 \times \cancel{6!}}{\cancel{6!} \times 2 \times 1} = \frac{8 \times 7}{2}$$ 5. **Evaluate:** $$= \frac{56}{2} = 28$$ **Answer:** There are 28 different combinations of six numbers chosen from digits 1 to 8 without repetition.