Question

1. true or false: picking the 1st, 2nd, and 3rd place winners at a track meet is an independent event.
2. a sandwich shop offers a choice of 4 types of bread, 8 types of meat, and 4 types of cheese. how many different sandwiches could be made with 1 type of bread, 1 type of meat, and 1 type of cheese?

Explanation:

Step1: Define independent events

Independent events are those where the outcome of one event does not affect the outcome of another.

Step2: Analyze track - meet winners

Picking the 1st - place winner affects the pool of candidates for 2nd and 3rd place. So, they are not independent.

Step1: Apply multiplication principle

The multiplication principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then there are \(m\times n\times p\) ways to do all three things together.

Step2: Identify values

Here, \(m = 4\) (types of bread), \(n=8\) (types of meat), and \(p = 4\) (types of cheese).

Step3: Calculate

The number of different sandwiches is \(4\times8\times4=128\).

Answer:

False