I'm struggling on these 2 problems:
-
How many 16 bit strings are there containing six 0's and ten 1's
with no consecutive 0's? -
How many 8 bit strings with exactly 2 1's are there such that the 1's
are not adjacent?
For the first one, I am guessing they must alternate between 0 and 1 but I have no clue how to set this up. How can I use combinations to find this?
Best Answer
Don't space out; select the spaces! Put
0
,0
,0
,0
,0
, and0
into_1_1_1_1_1_1_1_1_1_1_
You have ten
1
and eleven spaces to place the six0
such that only one0
goes in any space. How many ways can you select six of these eleven spaces?Second verse, same as the first. (Only the numbers are changed.)