Answer to Question #320216 in Python for ali

Question

By both generating and directly computing obtain the number of the following:

a. All permutations of (0,1,2,3,4,5).

b. All permutations of ("A","B","C").

c. Permutations of size 3 of (0,1,2,3,4,5).

d. Permutations of size 2 of (0,1,2,3,4,5,6).

e. Combinations of size 3 of (0,1,2,3,4,5).

f. Combinations of size 2 of (0,1,2,3,4,5).

g. Combinations of size 5 of (0,1,2,3,4,5)

Answer 1

def permutation(L, n):
    if n == 0:
        yield tuple()
        return
    for i in range(len(L)):
        x = L[i]
        LL = L[:i] + L[i+1:]
        for P in permutation(LL, n-1):
            yield tuple([x] + list(P))


def combination(L, n):
    if n == 1:
        for x in L:
            yield (x,)
    else:
        for i in range(len(L)+1 - n):
            x = L[i]
            for C in combination(L[i+1:], n-1):
                yield tuple([x] + list(C))
            


print('=========== a ============')
L = (0, 1, 2, 3, 4, 5)
cnt = 0
for p in permutation(L, len(L)):
    cnt += 1
print(f'The number of all permutations of {L} is {cnt}')


print()
print('=========== b ============')
L = ("A", "B", "C")
cnt = 0
for p in permutation(L, len(L)):
    cnt += 1
print(f'The number of all permutations of {L} is {cnt}')    


print()
print('=========== c ============')
L = (0, 1, 2, 3, 4, 5)
n = 3
cnt = 0
for p in permutation(L, n):
    cnt += 1
print(f'The number of permutations of size {n} of {L} is {cnt}')


print()
print('=========== d ============')
L = (0, 1, 2, 3, 4, 5, 6)
n = 2
cnt = 0
for p in permutation(L, n):
    cnt += 1
print(f'The number of permutations of size {n} of {L} is {cnt}')    


print()
print('=========== e ============')
L = (0, 1, 2, 3, 4, 5)
n = 3
cnt = 0
for c in combination(L, n):
    cnt += 1
print(f'The number of combinations of size {n} of {L} is {cnt}')  


print()
print('=========== f ============')
L = (0, 1, 2, 3, 4, 5)
n = 2
cnt = 0
for c in combination(L, n):
    cnt += 1
print(f'The number of combinations of size {n} of {L} is {cnt}')


print()
print('=========== g ============')
L = (0, 1, 2, 3, 4, 5)
n = 5
cnt = 0
for c in combination(L, n):
    cnt += 1
print(f'The number of combinations of size {n} of {L} is {cnt}')