Palmer and teller go to the local ice cream parlor after work that offers 40 flavors of ice cream. Palmer wants a cone with chocolate mousse on top, cherry truffle in the middle, and double Dutch chocolate on the bottom. Teller wants a dish with strawberry, banana, and vanilla. Just when they finish ordering, the lights go off and it is completely dark. The ice cream scooper can find the dishes and the cones, but must scoop the ice cream at random in the dark. What is the probability that:

A. Teller gets exactly what he wants?
B. Palmer gets exactly what he wants (order and all)?
C. Palmer does not get exactly what he wants?
D. If Palmer changes his order keeping the same ice cream flavors, but asking for them in a dish, does he have a better chance of getting what he wants? Explain.

To answer these probability questions, we need to analyze the given information and consider the number of possible outcomes.

First, let's determine the total number of possible outcomes. Since the ice cream scooper randomly scoops the ice cream in the dark, each scoop has equal probability of being any flavor. Therefore, for each serving (cone or dish), there are 40 possible flavors to choose from.

A. Teller's Order:
Teller wants a dish with strawberry, banana, and vanilla. Since there are 40 flavors and Teller wants 3 specific flavors, the probability that Teller gets exactly what he wants can be calculated as follows:

Number of favorable outcomes (3 specific flavors): 1
Total number of possible outcomes: 40 * 40 * 40 = 64,000

Probability of Teller getting exactly what he wants: 1/64,000

B. Palmer's Order:
Palmer wants a cone with specific flavors arranged in a certain order. So, there is an additional factor to consider – the order of the flavors. For each scoop, there are still 40 possible flavors to choose from, but the order matters. Therefore, the probability that Palmer gets exactly what he wants (order and all) can be calculated as follows:

Number of favorable outcomes: 1 (since there is only one specific combination of flavors out of 40 * 40 * 40 = 64,000 possible combinations)
Total number of possible outcomes: 64,000

Probability of Palmer getting exactly what he wants: 1/64,000

C. Palmer's Order (Not exact):
To calculate the probability that Palmer does not get exactly what he wants, we subtract the probability of him getting exactly what he wants from 1 (since 1 represents certainty or all the possible outcomes). So, we have:

Probability of Palmer not getting exactly what he wants = 1 - (1/64,000) = 63,999/64,000

D. Changing Palmer's Order to a Dish:
If Palmer changes his order to a dish, the flavors can be in any order, which eliminates the need to worry about the specific order of the flavors. When flavors can be in any order, the calculation is simplified.

For each serving (dish), there are still 40 possible flavors to choose from. Palmer wants three specific flavors, so the probability that Palmer gets exactly what he wants (regardless of the order) can be calculated as follows:

Number of favorable outcomes (3 specific flavors): 1
Total number of possible outcomes: 40 * 40 * 40 = 64,000

Probability of Palmer getting exactly what he wants (regardless of the order): 1/64,000

Conclusion:
Based on the calculations:

A. The probability that Teller gets exactly what he wants is 1/64,000.
B. The probability that Palmer gets exactly what he wants (order and all) is 1/64,000.
C. The probability that Palmer does not get exactly what he wants is 63,999/64,000.
D. Changing Palmer's order to a dish does not affect the probability of getting exactly what he wants.