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Between 700 and 900 means that both of them are not included. Instead we should start at 701 up to 899. 

a) Since the numbers that begin with 8 are in the range of 800-899 meaning 100 numbers.

b) Numbers that end in 8 as of 700:
708,718,728,738,748,758,768,778,788,798 meaning there are 10 numbers ending with 8 each hundred. Therefore we have an answer of 20 numbers that ends with 8 because there is also 808, 818,828, and so on