A box contains 25 apples, of which 20 are red and 5 are green. Of the red apples, 3 contain maggots and of the green apples, 1 contains maggots. Two apples are chosen at random from the box. Find the probability that both apples are red and at least one contains maggot.

$\displaystyle P(Both red and at least one maggot) = P(Red, Red Maggot)+P(Red maggot,Red)+P(Red Maggot,Red Maggot)$

$\displaystyle =\frac{20}{25} \times\frac{3}{24}+\frac{3}{25}\times \frac{19}{24}+\frac{3}{25} \times \frac{2}{24}$

$\displaystyle =\frac{41}{200}$

but answer is 9/50