Answer
The number of four letter passwords = $7_{{P}{_{4}}}$ = 840
Work Step by Step
Total number of letters =A, B, C, D, E, F, G = 7
Number of letters to form password = 4
To find the number of four letter passwords among seven letters without repetition, we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)! }$
The number of four letter passwords = $7_{{P}{_{4}}}$ = $\frac{7!}{(7 - 4)!}$
= $\frac{7!}{3!}$
= $\frac{7\times6\times5\times4\times3!}{3!}$
= $7\times6\times5\times4$
= 840
