5-letter strings using the letters in the word "EVERGREEN" From the word EVERGREEN, 5 letters are chosen at random and arranged into a string of letters. What is the probability that this string is palindromic?

in the case that the probability distribution is not uniform, one may find an elegant answer via the use of a tree diagram. Possibilities are: ERERE, EEXEE, ERXRE, REEER, REXER, where X is an element of the set {V,G,N}. Computing possibilities gives $\frac{1}{42}$

Edit: in the case of EEXEE, R may also be chosen. But the general solution is the same , as is the answer: simple tree diagram combined with multiplication principle.