Seven people including Bush and Putin are to be seated at a round table. In how many ways can the seating plan be arranged such that there is exactly one person who sits between Bush and Putin?
+23252 If there is no difference between looking at the picture in a clockwise manner or an anti-clockwise manner, there are 5 persons who can be the individual placed between B and P. Of the four remaining, any of four can be placed next to B, any of three can be placed next to that person, any of two can be placed next to that person, and there is one person remaining to be placed next to P. (There is no difference if you start with P instead of B.)To find the total number of ways, multiply these choices together: 5 x 4 x 3 x 2 x 1 = 120 ways. If there is a difference beween listing them clockwise and anticlockwise, multiply that answer by 2.
+23252 If there is no difference between looking at the picture in a clockwise manner or an anti-clockwise manner, there are 5 persons who can be the individual placed between B and P. Of the four remaining, any of four can be placed next to B, any of three can be placed next to that person, any of two can be placed next to that person, and there is one person remaining to be placed next to P. (There is no difference if you start with P instead of B.)To find the total number of ways, multiply these choices together: 5 x 4 x 3 x 2 x 1 = 120 ways. If there is a difference beween listing them clockwise and anticlockwise, multiply that answer by 2.
+129849 Anchor Bush and Putin in their seats.....but remember ....we can seat them in 2 ways.....Bush to Putin's left or vice-versa....
Any of 5 remaining people can be chosen to sit between them = 5 ways
And the remaining people can be seated in 4! ways = 24 ways
So 2 * 5 * 24 = 240 arrangements
