5. You are scheduling your classes for next year. There are 4 required classes: a physical education class, a history class, an english class, and a math class. You can choose from 5 physical education
classes, 6 history classes, 5 english classes, and 3 math classes. In how many different ways could
you select the 4 required classes?

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Explanation:

For now, let's consider we can only select 2 classes instead of 4. Let's say we only had to worry about PE and history.

Let A,B,C,D,E represent the five PE classes.

Let F,G,H,I,J,K represent the six history classes.

If you arrange the letters in a table, you should get 5*6 = 30 different inner boxes of the table. Refer to the diagram below.

Each two letter code in the table represents the 2 class combo. For example, BG means you picked PE class B and history class G.

This idea can be extend to selecting 3 classes. Imagine that each of the codes in the table are laid along the side of a new table. So we'd have a table of 30 rows. Then lay out 5 columns (say with letters L,M,N,O,P) to represent the 5 English classes. You would get a table of 30*5 = 150 different combos here. Of course you shouldn't actually make such a table since it's so large, but I'm simply just saying for you to imagine one. All of the tables mentioned are completely optional. A tree diagram is another way to organize things, though tree diagrams tend to get cumbersome.

Anyway, we would have 5*6*5 = 30*5 = 150 different ways to pick the PE, history and English classes. We can extend this out to include the math classes as well.

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In short, all we do is multiply the given values together:

5*6*5*3 = 30*15 = 450

This idea is known as the counting principle.

6.9

step-by-step explanation:

simple math really

6 1/2 times 0.6 = 3.9

but if you are just doing 6 and not 6 1/2 then the answer is 3.6

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.