Question

How many 8-bit strings contain 5 or more 1’s?

Answer 1

Here we need to find how many 8-bit strings contain 5 or more 1's.

We know that a byte is a string of 8 bits and bit string contains 0 or 1.

Now a 8-bit string is entirely determined by the location of the 1's

Case 1: There are 5 1's.

Now number of ways by which we can arrange 5 1's in 8 positions is=

Case 2: There are 6 1's.

Now number of ways by which we can arrange 6 1's in 8 positions is=

Case 3: There are 7 1's.

Now number of ways by which we can arrange 7 1's in 8 positions is=

Case 4: There are 8 1's.

Now number of ways by which we can arrange 8 1's in 8 positions is=