Question 1011085: if you know the names of the remaining 8 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 40320 possible arrangements.
that would be 8!
the probability of picking the correct order randomly would be 1 / 40320 = .0000248015873.
in order words, the probability of picking the correct order on a random basis, such as picking the names out of a hat, is not very good.
for example:
suppose there were only 3 reamining candidate.
3! = 3*2 = 6
there would be 6 possible arrangements.
if the candidates were abc, then the 6 possible arrangements would be:
abc
abc
bac
bca
cab
cba
for 4 candidates, multiply 6 * 4 = 24
then 5 * 24 = 120
then 6*120 = 720
then 7*720 = 5040
then 8 * 5040 = 40320
1 / 6 is manageable.
1 / 24 less.
1 / 8 becomes pretty impossible.
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