To calculate $10! - 7! \times 6!$, we first need to calculate each factorial and then perform the operations.

Step 1: Calculate Factorials

1. 10! (10 factorial):
   $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800$

2. 7! (7 factorial):
   $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5,040$

3. 6! (6 factorial):
   $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$

Step 2: Multiply $7!$ and $6!$

$7! \times 6! = 5,040 \times 720 = 3,628,800$

Step 3: Subtract

Now we have: $10! - (7! \times 6!) = 3,628,800 - 3,628,800 = 0$

Final Answer:

$10! - 7! \times 6! = 0$

Would you like further details or have any questions?

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Here are some related questions:

1. How would this calculation change if we used $11!$ instead of $10!$?
2. What if we had to calculate $10! + 7! \times 6!$ instead?
3. How would we approach a similar problem with exponents instead of factorials?
4. What are common applications of factorials in probability and combinatorics?
5. Can factorials be extended to non-integer values?

Tip: Factorials grow very quickly, so understanding their values for small numbers helps simplify larger calculations!