Let an 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 bn = the number of such n-digit integers ending with digit 1 and cn = the number of such n-digit integers ending with digit 0. The value of b6 is

To find b6, we have to find all 6 digit numbers ending with '1' such that no consecutive digits are '0'. Some of the examples possible are :

1. 1 0 1 1 1 1
2. 1 0 1 0 1 1
3. 1 1 1 1 1 1
   Three cases possible:
4. One zero- It can be placed in any of the four places. So, we get '4' such six digit numbers.
5. Two zeros- We get '3' such six digit numbers possible.
6. No zeros- We get only '1' such six digit number.
   Hence b6 = 4 + 3 + 1 = 8