Ketaki M. answered • 07/31/15

Tutor

New to Wyzant
Ketaki M Math,SAT,ACT.GRE,AP CAlculus

think of the 8 places to be filled by the students as first ,second,third.... eighth..

now the first place can be filled in 8 ways ie any one of the eight available

for the second place there are 7 people available and so on,....

for the last place only 1 person will be available...

now the fundamental principle of counting states that if 1 event can take place in m different ways ,corresponding to which another event can take place in 'n' diiff ways,then the total no of ways of occurance of both the events simultaneously is m*n..

we will apply the same principle here to fill all the 8 places.

so filling of the 8 places can be done in 8*7*6*.....*1 which is called 8 factorial...

out of these 8 factorial ways,half of the times peter will be ahead.. so your ans is 8!/2