A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

If the letters of the word 'TIRUPATI' are written down at random, then what is the probability that both Ts are always consecutive?

Let $m = 77^n$. The index $n$ is given a positive integral value at random. What is the probability that the value of $m$ will have $1$ in the units place?