MHB Finding the Number of Bit Strings with 8 Zeros and 10 Ones

[alexmahone]

How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?

 

[I like Serena]

How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?

Attempt? (Wondering)

 

[alexmahone]

Attempt? (Wondering)

x01x01x01x01x01x01x01x01x

I thought that since there are 9 positions for the 9th 1 and 8 positions for the 10th 1, there would be 9x8=72 strings. But this is just wrong since the 1s are indistinguishable.

 

[I like Serena]

x01x01x01x01x01x01x01x01x

I thought that since there are 9 positions for the 9th 1 and 8 positions for the 10th 1, there would be 9x8=72 strings. But this is just wrong since the 1s are indistinguishable.

Two scenarios: either one of those x'es is 11 and the others are empty, or 2 of those 9 x'es are 1. (Thinking)

 

[mrtwhs]

My thinking goes like this.

You have ten objects to arrange: (01),(01),(01),(01),(01),(01),(01),(01),1,1

So the answer is $$\dfrac{10!}{8!2!}=45$$