Problem: employees of a certain company are each to receive a unique 9 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Rationale: "there are 7 ! ways to make codes starting with 12 . there are 7 ! ways to make codes starting with 24 . there are 7 ! ways to make codes starting with 36 . there are 7 ! ways to make codes starting with 48 . the number of codes is 4 * 7 ! = 20,160 . the answer is d ."
annotated_formula: multiply(multiply(2, 3), 2)