Let a n denote the number of all n -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let b n = the number of such n -digit integers ending w

Question

Let a n ​ denote the number of all n -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are 0 . Let b n ​ = the number of such n -digit integers ending with digit 1 and c n ​ = the number of such n -digit integers ending with digit 0 . Question: Which of the following is correct?

TestHub · Accepted Answer

By recurring formula, a 17 ​ = a 16 ​ + a 15 ​ is correct Also c 17 ​  = c 16 ​ + c 15 ​ ⇒ a 15 ​  = a 14 ​ + a 13 ​ ( ∵ c n ​ = a n − 2 ​ ) ∴ Incorrect Similarly, other parts are also incorrect.

Mathematics - Permutation Combination Question with Solution | TestHub

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