def distObjIndistBox(n, r):
result = 0
for j in range(1, r + 1):
s = 0
for i in range(j):
s += math.pow(-1, i) * rCombinNoRep(j, i) * math.pow(j - i, n)
result += s / fact(j)
return result
def rPermutNoRep(n, r):
return (fact(n) / fact(n - r))
def distObjDistBox(n, r):
d = 1
for x in r:
d *= fact(x)
return fact(n) / d
def rCombinRep(n, r):
return fact(n + r - 1) / (fact(r) * fact(n - 1))
def rCombinNoRep(n, r):
return (rPermutNoRep(n, r) / fact(r))
def numOfDerang(num):
return fact(num) * probOfDerang(num)
def probOfDerang(num):
s = 1
for i in range(1, num + 1):
s += (math.pow(-1, i) * (1 / fact(i)))
return s