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

TIRUPATI has 8 letters with T appearing twice and I appearing twice. Total arrangements = 8!/(2!·2!) = 10080. Treating both Ts as one unit, we have 7 items (TT, I, R, U, P, A, I) with I repeated twice. Arrangements = 7!/2! = 2520. Probability = 2520/10080 = 1/4.