The 8 leaders of the G8 nations convene in Rome and stand in a row as they get ready to have some pictures of them taken by the press. What is the probability that the picture that the New York Times' editors will randomly select for publishing the next day is one in which Berlusconi is not standing next to Obama? (assuming that there are pictures of all possible standing arrangements).	Choose the correct choice from the following answers
A) 1/8
B) 1/4
C) 1/2
D) 3/4
E) 7/8
We'd have 7 units: 1, 2, 3, 4, 5, 6, and {Berlusconi, Obama}. These 7 units can be arranged in 7! ways. Berlusconi and Obama within their unit can be arranged in 2! ways. Thus the total number of ways to arrange 8 leaders so that Berlusconi and Obama to stand together is 7!*2!.   8 people without any restriction can be arranged in 8! ways, thus in 8! - 7!*2! arrangements Berlusconi and Obama will not not be standing together.   P=8!−7!∗2!8!=1−7!∗2!8!=1−14=34P=8!−7!∗2!8!=1−7!∗2!8!=1−14=34.   Answer: 3/4.
<result>D</result>
The 8 leaders of the G8 nations convene in Rome and stand in a row as they get ready to have some pictures of them taken by the press. What is the probability that the picture that the New York Times' editors will randomly select for publishing the next day is one in which Berlusconi is not standing next to Obama? (assuming that there are pictures of all possible standing arrangements).