Question

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).

Answer 1

The required probability is
`(3)/(4)`.

Explanation:

Consider the provided information.

There are 8 leaders.

Thus, the total number of ways to arrange 8 leaders are 8!.

Assume that Obama and Berlusconi is one person.

Therefore the total number of leaders are 7 (As Obama and Berlusconi is one person).

The number of ways in which 7 leader can be arranged: 7!

Although Obama and Berlusconi is one unit but they can interchange their place in 2 ways. Like Obama and Berlusconi or Berlusconi and Obama

That means the total number of ways : 7!×2

The number of ways in which they are not next to each other = Total number of ways - The number of ways in which they are next to each other

Number of ways they are not next to each other = 8!-7!×2

The probability that they are not next to each other =
`(8!-7!*2)/(8!)=(3)/(4)`

Hence, the required probability is
`(3)/(4)`.