AP EAMCET2009MathematicsPermutation and Combination
A binary sequence is an array of 0's and 1's. The number of n -digit binary sequences which contain even number of 0's is
Options
- A2^ n-1
- B2^n-1
- C2^ n-1 -1
- D2^n
Correct answer
A. 2^ n-1
Step-by-step solution
The required number of ways = The even number of 0 's ie, 0,2,4,6, aligned & = n ! n ! + n ! 2 !(n-2) ! + n ! 4 !(n-4) ! & = ^n C₀+ ^n C₂+ ^n C₄+ =2^ n-1 aligned