I don't understand how to get this answer.?

Question

Suppose a traveler wanted to visit a museum, an art gallery, and the state capitol building. 45-minute tours are offered at each attraction hourly from 10 a.m. through 3 p.m. (6 different hours). Solve the problem, disregarding travel time.
In how many ways could the traveler schedule all three tours in one day, with the museum tour being after noon?

Please explain it to me if u can.

Thnak you.

Answer 1

alright I'll try my best.
each hour a tour starts at each place and the tours are less then an hour.
now we figure out the poisble number of things that could be scheduled for each hour with the musem tour being after noon, and not going on a tour a fourth option so for the
10 am hour 3 poisabitiles
11 am hour 3 poisabitiles
noon 4 poisabities
1 pm hour 3 poisabitiles
2 pm hour 2 poisabities
3 pm hour 1 poisabitie

only for noon is there all 4 optoins (one of the three tours or no tour) and every hour after that there is one less optoin, because the day is coming to an end. next step, I belive is to mutiply the optoins for each hour
3*3*4*3*2*1= 216
and that would be the number of differnt ways a traveler could schedule all 3 tours in one day, I do belive

edit: after reading the logic in the other answers, my answer is only partually correct, in that my answer only works if each of the off hours get scheduled for something specail that could take place at any hour but could be differnt each hour. if it's just the tours there's just 80 poisable ways like the guy above me said

Answer 2

Hi Courtney,

We'll assume here that "after noon" means that the only times we can consider are 1:00 PM, 2:00 PM, and 3:00 PM. So, considering the museum tour first, there are only those three choices. Now, that leaves 5 hours left for either of the two remaining tours. Taking the art gallery next, we have 5 different time slots available. For the capitol, that leaves 3 slots left.

So, our answer is

3 X 5 X 4 = 60 different ways.

In our problem, each choice is independent of the other; we could have chosen them in any order, with the only constraint being on the museum tours.

If something can be done in m different ways, and another in n different ways, then both of them can be done in m X n different ways. This is called the multiplication rule, or the mn rule.

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If "after noon" means the time slots of 12:00PM, ... 3:00PM, then we can schedule the museum tour in 4 different ways, and the multiplication is

4 X 5 X 4 = 80 different ways.

James :-)

Answer 3

There are 4 different museum tours (12-1,1-2,2-3,3-4). For each of these, an art gallery can be toured in 5 different time slots, and once the art gallery is chosen, the capitol can be toured in 4 different slots. NOTE, this includes "time outs" where nothing is toured. So the total is 80 or 4 * 5 * 4

Answer 4

there are 3 times to tour the museum: 1, 2, 3
for any of these, there are 5 times to visit the art gallery.
however you chose the preceding, there are 4 times to visit the capitol.
So the number of possibilities = 3 * 5 * 4 = 60