45. Which of the following is equal to (3!)! / 3!?
Answer: D
5!
Calculating (3!)! / 3! results in 5. The value of 3! is 6, so (3!)! is 6! which equals 720. Dividing 720 by 6 gives 120, which is equal to 5!.
A) 2!
This option is incorrect as 2! equals 2. The calculation of (3!)! / 3! results in 120, which is much greater than 2.
B) 3!
This option is incorrect because 3! equals 6. The value of (3!)! / 3! equals 120, which is significantly higher than 6.
C) 4!
This option is incorrect as 4! equals 24. Comparing 24 to 120 shows that 4! does not equal the result of (3!)! / 3!.
D) 5!
This option is correct because 5! equals 120. The calculation of (3!)! gives 720, and when divided by 6, results in 120, confirming that (3!)! / 3! equals 5!.
E) 6!
This option is incorrect since 6! equals 720. The calculation shows that (3!)! / 3! equals 120, which does not match the value of 720.
Conclusion
The correct answer is 5! because it directly corresponds to the calculated value of (3!)! / 3!, which equals 120. All other options fail to match this result, confirming that D is the only valid choice.