All the letters of the word SUCCESS are arranged at random in a row. What is the probability that the three S's stand together?

SUCCESS has 7 letters with S three times and C twice, so the number of distinct arrangements is 7!/(3!·2!) = 5040/12 = 420. Tying the three S's into one block leaves the five items [SSS], U, C, C, E, arranged in 5!/2! = 60 ways, so the probability is 60/420 = 1/7. Forgetting that the two C's are alike in that block count gives 120/420 = 2/7, and 3/7 is only the fraction of the letters that happen to be S. A neat check: the S's take 3 of the 7 places in C(7,3) = 35 equally likely ways, and 5 of those place-sets are runs of three in a row, so the answer is 5/35 = 1/7 — while 1/35 would count just one of those five runs.