(CMR 2004) - Question Medium of Mathematics

In a school presentation, eight friends, including Carlos, Timóteo, and Joana, line up. Calculate the number of different ways this line of friends can be formed so that Carlos, Timóteo, and Joana always stay together:

A store offers a 20% discount on all products, and a second 10% discount for cash payments. What is the final price of a product that cost R$100.00 and was bought in cash?

In a school, a survey was conducted on students who practiced sports. It was found that 60% of the students practiced soccer, 30% practiced volleyball, and 20% practiced both sports. If a student is randomly selected, what is the probability that he practices soccer, given that he practices volleyball?

A store decides to reward its customers. Each customer will receive one of the six possible gifts available, according to their arrival order at the store. The gifts to be distributed are: a ball, a keychain, a pen, a soda, an ice cream, and a CD, in that order. The first customer at the store receives a ball, the second receives a keychain, the third receives a pen, the fourth receives a soda, the fifth receives an ice cream, and the sixth receives a CD. The seventh receives a ball, the eighth receives a keychain, and so on, according to the order of the gifts. The one-thousandth customer will receive as a gift a: