Let $S$ be the set of permutations of the sequence $2, 3, 4, 5, 6$ for which the first term is not $2.$ A permutat

Let $S$ be the set of permutations of the sequence $2, 3, 4, 5, 6$ for which the first term is not $2.$ A permutation is chosen randomly from $S.$ The probability that the second term is $5$ is given by $\dfrac{a}{b}$ (in lowest terms). What is $a+b?$

(A) 5
(B) 6
(C) 11
(D) 16
(E) 19

Answer: E

Source: Veritas Prep

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