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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

DM-Probability -Q15


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+2 votes

A recurrence relation for the number of bit strings of length n that do not contain three consecutive 0s. T(n) represents number of such bit strings of length n.

(A).T(n) = T(n-1) + 2T(n-2)

(B).T(n) = T(n-1) + T(n-2) + T(n-3)

(C).T(n) = T(n-1) + T(n-3)

(D).T(n) = 2T(n-1) + T(n-3)

asked Jul 7, 2020 by gbeditor-2 (72,840 points)
reshown Jul 10, 2020 by gbeditor-2

1 Answer

0 votes

Easiest way is 

f(1) is 2 namely 0 and 1

f(2) is 4 namely 00, 01, 10 and 11

f(3) is 001, 010,011,100,101,110,111 which is 7 as we didn't include 000

f(4) = all strings except for 0000,1000 and 0001 which is 16-3 = 13

 

Also, I am able to see a recurrence relatIon here

f(4) = f(3) + f(2) + f(1) 

For fun, solving for f(5)

All 5 bit strings except for 00000,00001,00010,00011,01000,10000,10001,11000 

which is 32-8 which is 24

Now you can see it is 13+7+4 = 24

Yippie,

B is the answer.

answered Oct 13, 2020 by tsshashankrustagi (11,240 points)
Answer:

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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