Question

Please help me! I do not understand one of the questions and it would be outstanding if you could help me! I'm sorry if I seem a little desperate, I've been working on this quiz for the past hour.

Dan wants to arrange his red, blue, and green bags in a row on a shelf, where R is red, B is blue, and G is green. Which tree diagram best shows the sample space of all the possible ways to arrange the three bags in a row on a shelf?

Option one: A tree diagram is shown. The lines branch out to R, B, and G. In the first row, the lines branch out from R to B to G and from R to G to R. In the second row, the lines branch out from B to R to G and from B to G to B. In the last row, the lines branch out from G to R to B and from G to B to R.

Option two: A tree diagram is shown. The lines branch out to R, B, and G. In the first row, the lines branch out from R to B to B and from R to G to B. In the second row, the lines branch out from B to R to B and from B to G to R. In the last row, the lines branch out from G to R to B and from G to B to R

Option three: A tree diagram is shown. The lines branch out to R, B, and G. In the first row, the lines branch out from R to B to G and from R to G to B. In the second row, the lines branch out from B to R to G and from B to G to B. In the last row, the lines branch out from G to R to B and from G to B to G.

Option four: A tree diagram is shown. The lines branch out to R, B, and G. In the first row, the lines branch out from R to B to G and from R to G to B. In the second row, the lines branch out from B to R to G and from B to G to R. In the last row, the lines branch out from G to R to B and from G to B to R.

Thank you in advanced for helping me, it really means a lot. I don't know where I would be without you all, thank you! <3

Answer 1

Answer: It's option 4

Step-by-step explanation: Let me fill you in on a trick I learned and why this is right so... every time you see a tree diagram like this you have to make sure that each letter across from each other match EX. P Q

Q P

See how p and p match across from each other that means it's correct here's why because each time you have a tree diagram you have EX. Q P but now you have to find another way you can make it and another way is to flip it when EX. Q P now if you flip it...

P Q

Now if you do this the letters end up matching every time which is how you know it's correct.

I know this looks long but its actually an easy trick to understand I hope you get what I'm saying hope this helps have a good day !

Answer 2

See the attached image. The tree should consist of paths (left-to-right) that exhaust all the possible arrangements. 3 choices for the first bag (R, G, or B), 2 choices for the second (color availability depends on the first bag), and 1 for the third (again dependent on previous color), so there are
`3\cdot2\cdot1=3!=6` possible arrangements/permutations.