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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 -Q16


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
+1 vote

C_n  represents the number of ways to parenthesize the product of n + 1 numbersx_0 . x_1 .x_2 .....x_n, to specify the order of multiplication. For example these are 5 ways to parenthesize x_0,x_1,x_2,x_3

image

The recurrence relation C_n can be expressed as 

(A).\sum_{k=0}^{n-1} C_k C_{n-k-1}

(B).\sum_{k=1}^{n-1} C_k C_{n-k-1}

(C).\sum_{k=0}^{n-1} C_k C_{n-k}

(D).\sum_{k=1}^{n-1} C_k C_{n-k}

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

1 Answer

0 votes

correct choice A

the number of ways of parenthesization possible is given by nth-catalan number

http://en.wikipedia.org/wiki/Catalan_number

 

answered Aug 24, 2020 by tsravishanker (320 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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