#please do not post homework
Kenneth Chan
Math 454
HW 5
1.P(n)= set of permutations 
Let P_i(n)= set of permutations where n happens to be in Location i
|P_i(n)|=P(n-1) for i=1,2..,n
|P(n)|=|P_1(n) union ... P_n(n)|=P_1(n)|+...+|P_n(n)|
P(n)=(1,2...,n)
P(n)=|P(n)|
2.P(n)= set of permutations 
Let P_i(n)= set of permutations where n happens to be in Location i
p(n)=p(n;a1,a2,a3):=(ka1,xa2,ya3)
(p(n)=(ka1))+(p(n)=(xa2))+(p(n)=(ya2))
p(n)=(ka1,xa2)+(ka1,ya2)+(xa2+ya2)
P(n)=-(ka1,xa2,ya3)
p(n;a1,a2,a3):= |P(n;a1,a2,a3)| 
4.the person is included twice in line 1,he is excluded once in line 2,
included none is line 3 and excluded none in line 4.
A person who is clever, strong, goodlooking and kindhearted is 
included 4 in line 1, he is excluded 6 times in line 2, he is included 4 times in line 3
and excluded once in line 4