Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 5 cannot be adjacent digits in the integer, how many 5-digit integers are possible?	Choices:	A) 48	B) 66	C) 76	D) 78	E) None of these
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 : None of these
<result>E</result>
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 5 cannot be adjacent digits in the integer, how many 5-digit integers are possible?