If x is the number of ways in which six women and six men can be arranged to sit in a row such that no two women are together and if y is the number of ways they are seated around a table in the same manner, then x: y=

Step-by-step solution

6 Boys can be seated in a row in 6_ P₆ ways =6 ! . Now, in the 7 gaps 6 girls can be arranged in 7_ P₆ ways. x=6 ! 7_ P₆ =6 ! 7 ! 6 Boys can be seated in a circle in (6-1) ! ways =5 ! Now, in the 6 gaps 6 girls can be arranged in 6_ P₆ ways. array llrl & & y=5 ! 6_ P₆ =5 ! 6 ! Now, & x: y=6 ! 7 !: 5 ! 6 ! & x: y=7 !: 5 ! & x: y=7 6 5 !: 5 ! & x: y=42: 1 array