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!

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- November 28th 2012, 05:37 PMwattskickinpermutation 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!

- November 28th 2012, 05:41 PMLinkRe: permutation problem
Because you have counted two times the permutations which start with 3 and end with 7 simultaneously.