Number of sub-sequences in a given sequence

Question

If I am given a sequence X = {x1,x2,....xm}, then I will have (2^m) subsequences. Can anyone please explain how can I arrive at this formula intuitivel

Answer 1

For each element in a sequence of length m, you can either select it or leave it. Thus, there are 2 ways to deal with each element. Therefore, the total no. of ways to deal with all the m elements is 2*2*2...... m times = 2^m times.