Kenneth Rosen Edition 7 Exercise 6.3 Question 35 (Page No. 414)

Question

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

Answer 1

Well, you have 8 01s and then 2 1s left over.

Say a = 01 and b = 1.

You are then basically looking to find the number of unique strings with 8 a's and 2 b's.

For example, aaaaaaaabb

C(10,8)=10*9/2=45