Let denote the number of all digit positive integers formed by the digits of both such that no consecutive digits in them are . Let the number of such digit integers ending with digit and the number of such digit integers ending with digit . The value of is
Explanation for the correct option:
Finding the value of :
Given denote the number of all digit positive integers formed by the digits
Therefor,
For total number since we have only '' as a positive integer formed by the digits
For total numbers As we have numbers
For total numbers As we have numbers
According to given information we will not take in above set because two consecutive digits are zero.
For total numbers As we have numbers
Observing , , , we get a relation
Also, given the number of such digit integers ending with digit
Similarly
Similarly we get the relation,
Substituting
Hence, option (B) is the correct answer.