The 8 leaders of the G8 nations convene in Rome and stand in a row as

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).

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8

Bunuel · Accepted Answer

Glue those two together. 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 = \frac{8! - 7!*2!}{8!}=1 - \frac{7!*2!}{8!} = 1 - \frac{1}{4} = \frac{3}{4} .

Answer: D.

CrackverbalGMAT · Answer

The 8 leaders of the G8 nations can stand in a row in 8! ways.

Lets remove Berlusconi and the other 7 people can stand in 7! ways.

Now Berlusconi can be added back just before or just after Obama, so there are 2 * 7! ways in which 8 persons can stand in a row, having Berlusconi next to Obama.

Probability that they stand next to each other =Favourable Cases/Sample space

= 2*7! / 8!

=1/4

Thus Probability that they do not stand next to each other = 1- 1/4

= 3/4

(option d)

D.S
GMAT SME

sumitkrocks · Answer

\frac{(8!-7!*2!)}{8!}  = \frac{ 3}{4}

Option (D) is correct

joohwangie · Answer

1-(7!*2)/8!

1-1/4

=3/4

D

sarthak1701 · Answer

Order Matters here.

There are 8 PERMUTATIONS in total = 8!

Now, let's consider O and B together = O B _ _ _ _ _ _

Number of ways in which O and B are together = 7!*2 (Multiply by 2 to account for the arrangements between O and B)

Ways in which O and B do not stand together = 1-7!*2/8! = 1-1/4 = 3/4

bumpbot · Answer

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