Final answer:
To calculate 7! / 3!, we evaluate the factorials and simplify the expression to find the answer.
Step-by-step explanation:
To calculate the value of 7! (7 factorial) divided by 3! (3 factorial), we need to evaluate the factorials first. The factorial of a number is the product of that number and all the positive integers less than it. So, 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1, and 3! = 3 × 2 × 1.
Now, substituting these values into the expression, we get:
startfraction 7!/3! = startfraction (7 × 6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1) = (7 × 6 × 5 × 4) / (3 × 2 × 1) = 1680.
Therefore, the answer is 1680 (option a).