All the letters of the word LEVEL are arranged at random in a row. What is the probability that the arrangement begins and ends with L?

LEVEL has 5 letters with L twice and E twice, so the number of distinct arrangements is 5!/(2!·2!) = 30. Fixing an L at each end leaves E, E, V in the middle, giving 3!/2! = 3 arrangements. Probability = 3/30 = 1/10.