Combinations Examples on Bit Strings

In this class, We discuss Combinations Examples on Bit Strings.

The reader should have prior knowledge of combinations formulae. Click here.

Example:

How many bit strings of length 8 contain the following?

1) Exactly five ones.

Here, to place 8-bit strings. We need eight positions.

We need to select five positions out of eight.

Place one’s in the selected positions, and zero’s in the remaining positions.

Different ways to select five positions is Ncr = 8c5.

Total ways = 8c5 = 56

2) Equal number of zeros and ones.

We need to take four one’s and four zero’s.

Select four positions from the eight positions.

To select four Ncr = 8c4.

Total selections = 8c4 = 70.

3) At least four ones.

We can consider four ones, five ones, six ones, seven ones, and eight ones.

The total selections are given as 8c4 + 8c5 + 8c6 + 8c7 + 8c8.

Total 163 selections possible.

4) At least three ones and at least three zeros.

The total possibilities are given below

three one’s and five zero’s

four one’s and four zero’s

five ones and three zeros.

Total = 8c3 + 8c4 + 8c5

= 182