Answer the following counting questions about bit strings. What is the number of 0/1 bit strings with 20 "0"s and 5 "1"s, so that there are no adjacent "1"s? (b) You want to count the number of 0/1 bit strings with 15 "0"s and 4 "1"s, so that between every two "l"s there are at least two "0"s. You want to count the number of bit strings of length 10 that contains 4 consecutive "1"s, c.g. 0001111110, 0011110010. Barry Bruin proposes the following: There are 7 possible starting positions of 4 consecutive "1"s, (it cannot start at the last 3 positions). Once we know where are the 4 consecutive "l"s, the remaining 6 bits can be either 0 or 1. Hence the answer should be 7 "middot 2^6. Explain why Barry Bruin is wrong, and calculate the correct