Calculate the value of B_6?
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 and B n denote number of such n Digit integers ending with digit 1 and C n denote number of such n Digit integers ending with digit 0. Then the value of B 6 is?
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1 solution
The first and last digit will have to be 1. The middle 4 digits have to be filled with 0 and 1
Let 1s be Xs and 0s be Ys
4X, 0Y = 1 way (1 1 1 1)
3X,1Y = 4 ways(1 1 1 0, 1 1 0 1, 1 0 1 1, 0 1 1 1)
2X, 2Y = 3 ways (1 0 1 0, 0 1 0 1, 0 1 1 0)
Note that there can't be 3 or more 0s as there will be no way to keep them non-adjacent.
Therefore, a total of 8 ways.