Questions: There are 192 cars in a mall parking lot. Bill is looking for his 5 friends' cars. If Bill randomly chooses 5 cars, what are the odds that those 5 cars belong to his friends? Select the correct answer below: 5:187 5:192 192: 187 7:187

Solution Steps

Bill is looking for 5 of his friends' cars. There is only 1 way to choose all 5 of his friends' cars out of 5 cars.

The total number of ways to choose 5 cars from 192 is given by the combination formula: ¹⁹²C₅ = 192! / (5! * 187!) = 1,689,461,712

The odds are the ratio of successful outcomes to unsuccessful outcomes. The number of successful outcomes is the number of ways to choose the 5 friend's cars, which is 1. The number of unsuccessful outcomes is the number of ways to choose 5 cars that are not his friends' cars.

Total ways to pick any 5 cars: 1,689,461,712

Ways to pick his friend's 5 cars: 1

Ways to pick 5 cars that are not his friend's cars: 1,689,461,712 - 1 = 1,689,461,711

So the odds are 1 : 1,689,461,711 which simplifies to approximately 1 : 1689461711.

However, the provided options seem to have an incorrect calculation for combinations as none of the provided options is correct. Out of the options provided, 5:187 is the closest answer as it represents the number of friend's cars (5) versus the number of cars that don't belong to his friends if 5 were chosen (192-5=187)

Final Answer: 5:187 (closest option provided. The actual odds are approximately 1:1,689,461,711.)