Here\'s a binary word of length 12: 001011010101. As you go from the first 0 dow
ID: 3027817 • Letter: H
Question
Here's a binary word of length 12: 001011010101. As you go from the first 0 down to the last 1, you can count a total of 6 0's and 6 l's, and as you count, the number of 0's is never less than the number of 1 's. How many binary words of length 12 have that property? ANS.:_______________ Show the "A number" of the Catalan sequence in OEIS:____________ Figure out all of Catalan numbers from b_0 up to b_12. ANS.:________________________________________ ______________________________________________ How many upright paths from (0, 0) to (6, 6) never cross the line y = x? ("Upright path" is defined in problem 3a.) ANS.:_______________________________Explanation / Answer
to find haw may binary word which have property that
total count of o's and 1's in b12 is same
that there is 6 0's and 6 1's
since b12 there is 12 positions of 0 or 1's
since number of 0's=number of 1's
we have 6 position which have each 2 choices
that is for 0's there are 6 position for 0's
each position have 2 choices
therefore choice of number of 6 0' and 6 1's =2x2x2x2x2x2
=64
therfore there are 64 binary numbers which have given properties