Let y = x! and z = (2x)! . If (z/y) = 120 , then what is the value of (3x)! ?

Step-by-step solution

Given y = x! and z = (2x)! . We are given z y = 120 . Substituting the values of y and z , we get: (2x)! x! = 120 Checking for small integer values of x : For x = 1 , 2! 1! = 2 For x = 2 , 4! 2! = 24 2 = 12 For x = 3 , 6! 3! = 720 6 = 120 Thus, x = 3 . We need to find the value of (3x)! . Substituting x = 3 , we get (3 3)! = 9! . 9! = 9 8 7 6 5 4 3 2 1 = 362880 . Answer: 362880