each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 5 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
"number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 5 are adjacent - consider 1 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 5 can be arranged as 15 or 51 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
subtract(multiply(multiply(multiply(5, 5), 1), const_2), multiply(multiply(multiply(5, 1), const_2), const_2))