Question

8. Show all computations for the following. Do not use a calculator.

(a) How many bit strings are there of length six which are palindromes? Explain

(b) How many bit strings are there of length 6 which contain exactly three 1’s? Explain

Answer 1

Answer:

a= 8 ways

b. 20

Step-by-step explanation:

Palindrome of length 6 means first three digits must be same as the last three in reverse. For example 123321 is palindrome of six digits.

There 2 bits 0 and 1

a.So each of first three digits can be filled in 2 ways

therefore, 2*2*2= 8 ways

number of different palindromes of 6 digits will be 8

b. In a 6 digit a palindrome there Are 6 spaces in which 3 spaces are to be filled with 1's

this cab be done in

$_{6}^{3}\textrm{C}= \frac{6!}{3!\times3!}$

= 20