How Many 5-permutations that contain at least one number are there for the following set {a,b,c,d,e,f,g,1,2,3,4,5}

gistfile1.py

from itertools import permutations

s = ['a','b','c','d','e','f','g',1,2,3,4,5]
perms = permutations(s,5)

# The following line does this:
# For each 5-permutation, see if there is an instance of an integer in it (isinstance).
# If there is, add one to a temporary list which we then sum to give the total count.
count = sum([1 for p in perms if sum([isinstance(_, int) for _ in p])])
print count

Prints 92520 when run

P(12,5) - P(7,5) seems like the obvious answer, since that is all sets of 5, minus all possible combinations which only have letters.

P(12,5) - P(7,5) = 92520