(a) How many bit string consist of from one through four digits? (Strings of different length are considered distinct. Thus 10 an 0010 are distinct strings.)
(b) How many bit strings consist of from five through eight digits?

(a)

To find how many bit strings consist of from one through four digits. (Strings of different lengths are considered distinct. Thus 10 and 0010 are distinct strings.)

Given information:

The number of bit strings of length one is 1_ or 0_, i.e. 2 ways.

Concept used:

P(n,r)=n!n−r!

Calculation:

The number of bit strings of length 2 is 4.

0 1, 0 0, 1 0, 1 1

The other way of explaining is that there are two places and each place has two.

∴ The total number of possibilities is 22=4

(b)

To find how many bit strings consist of from five throgh eight digits.