Hello, chickeneaterguy!

I have an imcomplete solution.

Maybe someone can finish it?

How many permutations of the English alphabet do not contain

any of the strings FISH, RAT, or BIRD?

No repetition . . . obviously.

There are permutations of the alphabet.

How many of thesecontain FISH, RAT, or BIRD?do

The permutation contains the string FISH.

FISH can appear in possible positions in the permutation.

The other 22 letters can be placed in orders. .[1]

. . Hence, FISH appears in: . permutations.

The permutation contains the string RAT.

RAT can appear in positions in the permutation.

The other 23 letters can be placed in orders.

. . Hence, RAT appears in: . permutations.

The permutation contains the string BIRD.

BIRD can appear in possible position in the permutation.

The other 22 letters can be placed in orders.

. . Hence, BIRD appears in: . permutations.

I thought the answer is: .

. . but it is wrong.

In [1] when the other 22 letters are placed,

. . theycouldinclude the strings RAT or BIRD (or both).

I tried to eliminate this duplication,

. . but got stuck in a tangled, sticky web.

Can anyone salvage my work?

Or simply find a better approach?