Let `a_(n)` denote the number of all n-digit numbers formed by the digits 0,1 or both such that no consecutive digits in them are 0. Let `b_(n)` be the number of such n-digit integers ending with digit 1 and let `c_(n)` be the number of such n-digit integers ending with digit 0. Which of the following is correct ?

Options

A. `a_(17)=a_(16)+a_(15)`
B. `c_(17)nec_(16)+c_(15)`
C. `b_(17)neb_(16)+c_(16)`
D. `a_(17)=c_(17)+b_(16)`

Answer

A

Explanation

by recurring formula `a_(17)=a_(16)+a_(15)` is correct.
also, `C_(17) ne C_(16)+C_(15) impliesa_(15) ne a_(14)+a_(13)` `[becauseC_(n)=a_(n-2)]`
`therefore`Incorrect, similarly, other parts are also incorrect.