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?

Step-by-step explanation:

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.

answer is 144

step-by-step explanation:

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3