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

Explanation

To solve the problem of finding the number of permutations of the letters `a, b, c, d, e, f, g` taken all together, while ensuring that neither the pattern `beg` nor the pattern `cad` appears, we can follow these steps:

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

\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \]
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