Probability (Random Sampling)

A car dealer buys back second hand (or used) cars made by Japanese, American and European manufacturers that account for 50%, 20% and 30% of the total number of cars bought back by the dealer respectively. The past records show that the proportion of the cars from Japanese, American and European manufacturers that are defective are 5%, 6% and 10%, respectively, and the overall proportion of the defective cars in the dealer is 6.7%. If the car dealer randomly draws 20 cars, find the probability that 10 of them are Japanese cars and 2 of these 10 cars are defective.

Please show the work clearly, thank you.

望高手解答, 萬分感謝