Question

In a G-20 meeting, there were total 20 people representing their own country. All the representatives sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharaf.

• A. $2\times (17!)$
• B. $2\times (18!)$
• C. $(3!)\times (18!)$
• D. $(17!)$

Answer 1

The correct option is B $2\times (18!)$

A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan and the third person, sitting between them, as a single personality, we can arrange them in 17! ways buy Musharraf and Manmohan can also be arranged in 2 ways.
$\therefore$ Required number of permutations $=18\times (17!)\times 2=2\times 18!$