permutation with probability

[bettysanchez]

A used car lot is organizing 5 different coloured cars in a row by the road to draw people into the store. What is the probability that the red car and the orange car are on the two ends of the row to make the display more appealing?

 

[Romsek]

a) how many ways can you put the red and orange car on the ends?

b) having placed those cars on the end how many ways can you arrange the remaining 3 cars in between them?

c) so how many ways can you arrange the cars to be more appealing?

d) what is the total number of ways you can arrange the 5 cars?

e) so what is the probability of an arrangement being appealing?

 

[bettysanchez]

a

a) how many ways can you put the red and orange car on the ends?

b) having placed those cars on the end how many ways can you arrange the remaining 3 cars in between them?

c) so how many ways can you arrange the cars to be more appealing?

d) what is the total number of ways you can arrange the 5 cars?

e) so what is the probability of an arrangement being appealing?

a) 2 ways?
b)3! ?
c)120?

 

[tkhunny]

Is there ALWAYS a red and an orange?

 

[Romsek]

a

a) 2 ways?
b)3! ?
c)120?

c) is incorrect. if I have to ways to arrange 2 of the cars, and 3! ways to arrange the 3 other cars for each of those, how many appealing arrangements are there? (hint: multiply 2 and 3!)

you should be able to answer (d) since you answered (b)
(e) is just a division

 

[Steven G]

3! = 6. So there are 6 ways to arrange the 3 middle cars. Now for each of the 6 ways of arranging the 3 middle cars we can then either put red in front and orange at the end (6 arrangements of the 5 cars) OR we can put the orange car in front and the red car at the end (6 arrangements of the 5 cars).

If you think the answer should be 120, 6 or any other number then you should be able to list them!

 

[Dr.Peterson]

A used car lot is organizing 5 different coloured cars in a row by the road to draw people into the store. What is the probability that the red car and the orange car are on the two ends of the row to make the display more appealing?

Just a side comment about the problem:

They are "organizing" the cars. They have an opinion about what is "more appealing". Nothing is said about anything being done randomly. So I think the probability is 100%!

One of my pet peeves is probability problems that assume everything people do is random, and never state that (counterfactual) assumption. The least they could do is to ask for the probability that they don't have to change anything because the cars already happen to be in what they consider an appealing order!