Question

3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together

Answer 1

2 Ladies sitting together can be selected in  ³P₂  = 6 Ways

now remaining 1 Lady can not sit adjacent to these ladies

so out of remaining 4 seats she can sit only on two seats

hence  ²P₁  = 2 Ways

so Ladies can sit in  6 * 2 = 12  Ways

for Three Gents  3 Seats are Left so gents can sit in ³P₃  = 6 Ways

Total Number of Ways = 12 * 6 = 72

Answer 2

not sure about the method