Which of the following is equal to (3!)! / 3!?

Rationale

(3!)! / 3! is equal to 5!

To solve the expression, we first calculate (3!), which equals 6. Thus, we need to evaluate (6! / 3!). Calculating (6!) gives us 720, and dividing by (3!) (which is 6) results in (720 / 6 = 120). The factorial of 5, or (5!), is also 120, confirming that the answer is indeed 5.

A (2!) YOUR ANSWER

Calculating (2!) results in 2, which is far less than 120. This choice does not account for the factorial growth rate, which quickly escalates beyond factorials of smaller integers.

B (3!) YOUR ANSWER

The value of (3!) is (6), which is also much smaller than 120. This choice fails to reflect the result of the original expression, as we are looking for a factorial greater than (3!).

C (4!) YOUR ANSWER

Calculating (4!) yields (24), which is still less than 120. Thus, this option does not satisfy the equation, as it is not large enough to match the evaluated value of (120).

D (5!) CORRECT

As previously determined, (5!) equals (120), which is exactly the result of evaluating ((3!)! / 3!). This option correctly matches the value derived from the expression.

E (6!) YOUR ANSWER

The value of (6!) is (720), which exceeds (120). This choice is incorrect as it represents a factorial that is significantly larger than the result of the original calculation.

Conclusion

The expression ((3!)! / 3!) simplifies to (120), which corresponds exactly to (5!). Each of the other choices represents factorials that are either too small or too large to match this value, confirming that option D is the correct answer. Understanding the rapid growth of factorials is crucial for solving such expressions accurately.

Which of the following is equal to (3!)! / 3!?

(3!)! / 3! is equal to 5!

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