Final answer:
The probability that six names will be drawn in alphabetical order is 1/720, which converts to approximately 0.14% when expressed as a percentage.
Step-by-step explanation:
The question is asking for the probability that six names drawn from a hat will be in alphabetical order. We start by considering that, for any random selection of six names, there is only one way to arrange these names alphabetically, which is the desired outcome. Since the names are drawn without replacement, each draw reduces the total number of possible names to choose from. However, no matter the order in which the names are drawn, there will always be only one alphabetical arrangement of those names.
To find the probability, we recognize that there is a total of 6! (6 factorial) different ways to arrange six names, as the first name can be any of the six, the second can be any of the remaining five, and so on, giving us a total of 6 x 5 x 4 x 3 x 2 x 1 arrangements. Since only one of these arrangements is alphabetical, the probability is 1 divided by 6!, or 1/720. To express this as a percentage, we calculate (1/720) x 100%, which is approximately 0.14%, rounded to the nearest hundredth of a percent.