Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 5 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible?  Select: A) 48 B) 66 C) 76 D) 78 E) 72
Number of arrangements using 5 distinct digits = 5!   Number of arrangements in which 4 and 5 are adjacent - consider 4 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, 4 and 5 can be arranged as 45 or 54.   Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72   Answer : 72
<result>E</result>
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 5 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible?