Exercise 2.3

 2(ii) Find the number of ways of arranging 7 gents and 4 ladies around a circular table if  no two ladies

wish to sit together 

2(iii) Find the number of ways of arranging 7 guests and a host around a circle if  2 particular guests wish to sit on either side of the  host. 

2(ii)no.of ways of arrangements 7 gents, 4 ladies around a table so that no two ladies sit together  7 gents can be arranged around a circle in $(7-1)!=6!\text{ ways. }$ In between 7 gents there are 7 places for arranging 4 ladies and can be arranged in ${}^{7}P_4$ ways
no.of permutations =6! x ${}^{7}P_4$
2(iii) consider two perticular gents G1,G2 and host (H) 

As one units
remaining 5 gents G₃,G₄,G₅,G₆,G₇ and 

can be arrange aroudn a circle in $(6-1)!=5!$
two guests on either side of host can be arranged in 2! ways no.of permutations $5!\times 2!=120\times 2=240.$