# How many bit strings are there containing # 0's, and # 1's… Counting Problem Help?

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?

Don't space out; select the spaces!   Put 0,0,0,0,0, and 0 into _1_1_1_1_1_1_1_1_1_1_
You have ten 1 and eleven spaces to place the six 0 such that only one 0 goes in any space. How many ways can you select six of these eleven spaces?
• No ... What are you even counting there? The count of ways to select 6 of 11 items is $^{11}\mathrm C_6$ – Graham Kemp Sep 17 '15 at 4:05