# Please do not post homework
# Ravali Bommanaboina, 9/27/2020, Assignment 5
#Question 1
#P(n) is the set of permutations of {1,...,n}
#the number of permutations can be described as n(n-1)*...*(1)
#this is because the number of possible choices decreases by one after each element of the sequence is determined
#therefore we can rewrite the P(n) as P(n)=n!

#Question 2
#P(n) is the set of all permutations of any length of positive integers that add up to n
#therefore we can call a function that iterates x for (1,...,n)
#for each iteration one digit from {1...n} gets added to the sequence and we get all permutations of this sequence that adds to n
#so when n=3 and x=1 then we get the {111}
#when x=2 then we get {12,21}
#when x=3 then we get {3}

#Question 4
#determining if someone is clever and good-looking neither strong nor kind
#how many time he is included in line 1 -> 2 times |C| + |L|
#how many time he is included in line 2 -> 1 time  |C intersect L|
#how many time he is included (again) in line 3 -> 0 times
#how many time he is included (again) in line 4 -> 0 times