Thread: permutation problem

How many permutations of the digits 0, 1, 2, . . . , 9 either start with a 3 or end with a 7?

I thought the answer would be 9!+9! but the answer key states it is 9!+9!-8!

what is the -8!

Because you have counted two times the permutations which start with 3 and end with 7 simultaneously.