Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 24 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 3 and 4 are adjacent - consider 3 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 3 and 2 can be arranged as 32 or 23 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : b"
annotated_formula: subtract(multiply(multiply(multiply(5, 24), 3), const_2), multiply(multiply(multiply(24, 3), const_2), const_2))