Permutations

[Merida]

The number of permutations of the set {1,2,…,n} such that no three of 1, 2, 3, 4, appear consecutively can be given as
n!+24(n-2)!+24(n-3)!
n!-24(n-2)!+24(n-3)!
n!+24(n-2)!-24(n-3)!
n!-24(n-2)!-24(n-3)!
n!+24(n-1)!+24(n-2)!
I don’t know where to start or how , it would be very helpful if someone would provide me a hint

 

[Romsek]

I think I'd try to determine how many permutations that you DO have 3 or 4 of {1,2,3,4} appearing consecutively and subtract that from the total number of possible permutations.