2017 NS 26

\(\text{What's described can happen in the following ways}\\ \text{All 3 tiles match on a letter}\\ \text{All 3 tiles match on a number}\\ \text{1 of the tiles match both the other two, but the other two do not match}\\ \text{There are three ways that the previous line can occur}\\ [(1,2),(1,3)],[(1,2),(2,3)],[(1,3),(2,3)]\)

\(P[\text{3 tiles match letter}]=\dfrac{4}{24}\dfrac{3}{23}= \dfrac 1 2 \dfrac{1}{23}\\ P[\text{3 tiles match number}] = \dfrac 1 2 \dfrac{1}{23}\\ P[\text{2 tiles match the other tile but not each other}] = \dfrac{8}{24}\dfrac{4}{23} = \dfrac 4 3 \dfrac{1}{23}\\ P[\text{what's described}] = 2 \times \dfrac 1 2 \dfrac{1}{23} + 3 \times \dfrac 4 3 \dfrac{1}{23} = \dfrac{1}{23}+\dfrac{4}{23} = \dfrac{5}{23}\)