10!/7! is equal to?

The correct answer is 720. The factorial notation (!) means multiplying all positive integers from the number down to 1. The expression 10! / 7! can be simplified by expanding the factorials and cancelling common terms.

Step-by-Step Solution

• Expand the Factorials:
  
  10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
  
  7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
• Cancel the Common Factor 7!:
  
  10! / 7! = (10 × 9 × 8 × 7!) / 7!
  
  The 7! in the numerator and denominator cancel out completely.
• Multiply the Remaining Numbers:
  
  10 × 9 × 8 = 720
• Verification:
  
  10! = 3,628,800 and 7! = 5,040.
  
  3,628,800 ÷ 5,040 = 720. Confirmed.

Thus, 10! / 7! equals 720.