Use R Programming please.

10. Write R program and find answers via simulation for the following situations. (a) What is the probability of having the same side come up 7 times in a row in 1000 coin tosses? (b) In six coin tosses, what's the chance of making a different side come up for each toss, that's, you never get two tails or two heads in a row? (c) Say a glass rod of 0.10 unit length drops and breaks into 5 random pieces. Write an R-program to find the probability that the smallest piece has length below 0.02. [5M]