A gentleman invites a party of 10 guests to a dinner and places 6 of them at one table and the remaining 4 at another , the tables being round . the number of ways in which he can arrange the guests is ........?
Number of ways in which he can divide the group in size of 6 and 4 is 6C4
each group can be arranged in (6-1)!+(4-1)! ways
therefore total number of ways = 6C4 x ( 5!+3!)