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  • The number of permutations of the letters a, b, c, d such that b does not follow a, and c does not follow b and d does not follow c, is<div class='qna-option'

The number of permutations of the letters a, b, c, d such that b does not follow a, and c does not follow b and d does not follow c, is

Option: 1

9


Option: 2

11


Option: 3

13


Option: 4

14


Answers (1)

best_answer

Case I : 

a x    

Here                                     x=c\: \text{or}\: d

                       Number of ways = 2

Case II : 

b y z  

\\Here \quad u=a or b\\ \\If \quad u=a, then \: p=d\\ \\and\: if \; u=b, then \: p=a \; or\: d\\ \\\therefore \quad Number \; of \; ways =3

Case III :

c u p  

\\Here \quad u=a \: or\: b\\ \\If \quad u=a, then p=d\\ \\and\; if u=b, then\: p=a \: or\: d\\ \\\therefore \quad Number \: of \: ways =3

Case IV: 

d q r s

\\Here \:q=a \:or \:b \:or\: c\\ \\If \:q=a, then r=c \: and \:s=b\\ \\If\: q=b, then \:r=a \:and \:s=c\\ \\If \:q=c, then\: r=a \:or\: b

(If r = a, then s = b (impossible)

and if r =b, then s = a (possible)

\therefore Number of ways = 3 

\therefore Total ways = 2+3+3+3=11 ways 

Posted by

Rakesh

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