PROBABILITY Probabilites of Opera ATTENTION If any theorem

PROBABILITY - Probabilites of Opera

ATTENTION: If any theorem, definition, lemma or formula is used in the answer, it should be stated and explained why it is been used. Even though the problem may look simple, this is a probability question. Solution needs to be shown STEP by STEP with MATHEMATICAL JUSTIFICATION. Solution wihtout detailed work won\'t be marked. Solution needs to show how and why. FORMAL ANSWER should be applied.

Prior to attending the Opera, five people leave their coats and hats in a cloakroom (each person leaves exactly one coat and one hat). After the Opera, each person collects one hat and one coat which are given to them in random order. What is the probability that exactly two people out of five receive their correct hat and coat?

Solution

the probability of getting exactly two people out of five receive their correct hat and coat is

ther are way 5C2=10 to pick the correct hat and coat