Find the number of permutations of letters `a ,n ,c ,d ,e ,f,g` taken all together if neither beg nor cad pattern appear.

Explanation

To find the number of permutations of the letters `a, n, c, d, e, f, g` taken all together, while ensuring that neither the pattern "BEG" nor "CAD" appears, we can follow these steps:

### Step 1: Calculate the total permutations of the letters
The total number of permutations of 7 distinct letters is given by the factorial of the number of letters.

\[ \text{Total permutations} = 7! = 5040 \]
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