Exercise 2.4

 (5) In how many ways the letters of the word 'ASSOCIATIONS' can be arranged so that

(i) all S's come together

(ii) the 2A's do not come together 

ASSOCIATIONS
Total no.of letters=12
no.of A 's=2
no.of S's=3
no.of O's=2
no.of I's=2
(i)All S's come together 
consider 3 S's as one units
(SSS),A,A,O,O,I,I,C,T,N
can be arrangemed in $=\frac{10!}{2!2!2!}$
(ii)2 A's do not come together arrangemet S,S,S,O,O,I,I,C,T,N in $\frac{10!}{3!\times 2!\times 2!}$ways
there are 11 places to arrange two A's in $\frac{{}^{11}P_2}{2!}$
no.of permutations=$\frac{10!}{3!\times 2!\times 2!}\times \frac{{}^{11}P_2}{2!}$