Determine a justification for how many different bit strings of length ten...

Determine an appropriate justification for how many different bit strings of length ten:

i) remain unchanged if it is reversed, ie first bit is like the last one, then the first one and the second last and so on., as is the case for example the strings 1011001101 and 0101111010.

ii) contains exactly two 1-bits must not be contiguous.

iii) contains either five consecutive 0-bits or five contiguous 1-bits.

Re: Determine a justification for how many different bit strings of length ten...

i) The set of palindromes of length 10 is in one-to-one correspondence with the set of strings of length 5.

ii) Suppose the position of the leftmost 1 is 1. How many possibilities are there for the second 1? What is the position of the leftmost 1 is 2, 3, ...?