A crate has 5 red and 3 green apples. Three apples are taken out one after the other without replacement. What is the probability that their colours alternate?

Explanation

1. 01

   Red, green, red: $\frac{5}{8} \times \frac{3}{7} \times \frac{4}{6} = \frac{60}{336}$; green, red, green: $\frac{3}{8} \times \frac{5}{7} \times \frac{2}{6} = \frac{30}{336}$.

2. 02

   $\frac{60 + 30}{336} = \frac{90}{336} = \frac{15}{56}$.