self doubt

Question

https://gateoverflow.in/43485/gate2008-79

explain this in some easy way i am not able to understand it even after watching solution.

Comments

 Xn denote the number of binary strings of length n that contain no consecutive 0s.

X₅  denote the number of binary strings of length 5 that contain no consecutive 0s.

ist condition :  all are 1's

                            1 1 1 1 1 -- > 1 string 

2nd condition :   Four  "1" and One -- > "0"

                                _1 _ 1 _ 1 _ 1_  =  5c1 = 5 string

3rd condition : Three "1" and two ---- > "0"

                              _ 1 _ 1 _ 1 _   = 4c2  = 6 string

4th condition : two "1" and three "0"

                                _1 _ 1 _ = 3C3 = 1 string

total string formed  = 1+ 5 + 6 + 1 = 13 strings formed

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Thanx magma brother nice approach ..

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but option is not matched 13 is not in the answer.

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Brother but 13 is the correct answer ....

given options are wrong