If stand for a three digit integer with a 7 in the i-th place.
Then means numbers with 7’s in the first and third place.
What you want is:
.
Firstly i was wondering whether someone could check if ive done this right...
Suppose f is the permutation (1, 2, 3, 4)(5, 6, 7)(8, 9)(10) of the set X = {1, 2, . . . , 10} and let g be the permutation (1, 4)(2, 7)(3, 10)(5, 9)(6, 8)
of X. Calculate f o g and g o f.
I got f o g = (1)(2 3 4 5 7 8 10)(6 9)
and g o f = (1 2 3 6 7 9 10)(4)(5 8)
Now the question i have no idea about...
Let S be the set of 3-digit decimal integers {000, 001, 002, . . . , 999}. Use Inclusion-Exclusion to find how many such integers contain at least one 7. (Hint. Let S1 be the subset of S consisting of elements with first digit equal to 7, etc.)
I have no idea how to use the inclusion-exclusion principle so can anyone help with that please?
cheers