Calculating Bit Strings of Length 7 & 10

hyderman
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hello

can some one explain this in details thank u

a- How many bit strings of length seven either begin with two 0’s or end with three 1’s?
]
b- How many bit strings of length 10 contain either five consecutive 0’s or five consecutive
 
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You need to show some work, but as a hint how many different bit strings are there of arbitrary finite length? How can you modify this to get the number of the strings specified in your post?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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