Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the24 cannot be adjacent digits in the integer, how many 5-digit integers are possible? Choose the correct choice from the following choices:
A) 48  B) 72  C) 76  D) 78  E) 90
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 : 72
<result>B</result>
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the24 cannot be adjacent digits in the integer, how many 5-digit integers are possible?