If you know the names of the remaining six students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?
$P($ selecting the correct spelling bee order) $=$
(Type an integer or a simplified fraction.)
Answer
Final Answer: The probability of randomly selecting an order and getting the order that is used in the spelling bee is \(\boxed{\frac{1}{720}}\).
Step 1 ：The probability of randomly selecting an order and getting the order that is used in the spelling bee is equivalent to the probability of randomly selecting one specific order out of all possible orders of the six students.
Step 2 ：The total number of possible orders of six students is given by the permutation formula, which is n!, where n is the number of students. In this case, n = 6, so the total number of possible orders is 6!.
Step 3 ：The probability of selecting one specific order out of all possible orders is therefore \(\frac{1}{6!}\).
Step 4 ：Final Answer: The probability of randomly selecting an order and getting the order that is used in the spelling bee is \(\boxed{\frac{1}{720}}\).
