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Warren has five vehicles: a blue convertible, a black sedan, a red coupe, a silver station wagon, and a blue SUV. If he drives a different car to work each day from Monday through Friday, in how many orders could he drive his five cars during a week if he always drives the convertible on Friday and won’t drive the same color vehicle on consecutive days?
  • a)
    6
  • b)
    18
  • c)
    24
  • d)
    120
  • e)
    144
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Warren has five vehicles: a blue convertible, a black sedan, a red cou...
Restrictions:
1. He always drives the convertible on Friday
2. Won’t drive the same color vehicle on consecutive days -> He will not drive the blue SUV on Thursday, as on Friday he always drives the Blue Convertible.

Based on the above restrictions, below are the options what he can drive on each day.

This is a perfect scenario to use the total arrangements minus bad arrangements approach.
First, find the total, given that the blue convertible is on Friday: 4 * 3 * 2 * 1 * 1 = 24.
 Next, let’s find the number of arrangements where the blue convertible is on Friday and the blue SUV is on Thursday, violating the second restriction: 3 * 2 * 1 * 1 * 1 = 6. Good = Total - Bad = 24 - 6 = 18.

Alternatively you can look at the number of allowable options on each day, in which case it's helpful to flip the week and think Friday through Monday since your main constraints are on Friday (has to be the convertible) and on Thursday (can't be the blue SUV since he's already driving the blue convertible the next day). This means that you have:

1 option Friday, 3 options Thursday (anything but the two blue cars), 3 options Wednesday (he's already slotted in the convertible and one other car for Friday/Thursday, but now the blue SUV is back in the pool), 2 options Tuesday (anything but the three cars already slotted), and 1 option Monday (whatever's left).
So that calculation is 1 * 3 * 3 * 2 * 1 = 18.
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Community Answer
Warren has five vehicles: a blue convertible, a black sedan, a red cou...
Calculating the Number of Possible Orders:
To calculate the number of possible orders in which Warren can drive his five cars during a week, we need to consider the given conditions:

Conditions:
1. He drives a different car to work each day from Monday through Friday.
2. He always drives the convertible on Friday.
3. He won’t drive the same color vehicle on consecutive days.

Analysis:
- Since he drives a different car each day from Monday to Friday, the order of cars for these weekdays can be arranged in 5! (5 factorial) ways, which is 5 x 4 x 3 x 2 x 1 = 120 ways.
- However, we need to exclude the cases where he drives the same color vehicle on consecutive days.
- If the convertible is driven on Friday, then the car driven on Thursday cannot be blue. Therefore, the car driven on Thursday can be any of the other 4 cars.
- Similarly, the car driven on Wednesday can be any of the remaining 3 cars (excluding the color driven on Thursday).
- The same logic applies to Tuesday and Monday.
- Therefore, the total number of valid orders satisfying all conditions is 4 x 3 x 2 x 1 = 24.

Final Answer:
Therefore, the total number of orders in which Warren can drive his five cars during a week, considering all given conditions, is 24, which corresponds to option B.
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Warren has five vehicles: a blue convertible, a black sedan, a red coupe, a silver station wagon, and a blue SUV. If he drives a different car to work each day from Monday through Friday, in how many orders could he drive his five cars during a week if he always drives the convertible on Friday and won’t drive the same color vehicle on consecutive days?a)6b)18c)24d)120e)144Correct answer is option 'B'. Can you explain this answer?
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