Question

How can you find the number of bit strings of length ten that either begin with 101 or end with 010 ?

Short answer

The number of bit strings of length ten that either begin with 101 or end with 010 is .

Step-by-step solution

Definition of Concept

String: A Number String is a collection of related math problems designed to teach number-based strategies. It is a 10- to 15-minute routine that can be used during math class. Gather students in an area where the entire class meets to prepare an area for using the number string.

Find the number of bit strings

Considering the given information:

Number starts with 101 or with 010.

Using the following concept:

n Objects in box can be placed in r ways.

The number of strings is =10

Case 1:

The string begins with 101.

7 Places are remaining which is to be filled with 0 or 1

So, number of arrangements$=2^7=128$

Case 2:

String ends with 010

First 7 places are remaining which is to be filled with 0 or 1 .

So, number of arrangements$=2^7=128$

Case 3:

String starts with 101 and ends with 010

Number of arrangements$=2^4=16$

So, total number of arrangement,

=128+128-16

=240

Hence, the number of bit strings of length ten that either begin with 101 or end with 010 is 240 .