Let \( S \) be the set of all passwords which are six to eight characters long, where each chara... VIDEO
Let \( S \) be the set of all passwords which are six to eight characters long, where each character is either an alphabet from \( \{A, B, C, D, E\} \) or a number from \( \{1,2,3,4,5\} \) with the repetition of characters allowed. If the number of passwords in \( \mathrm{S} \) whose at least one character is a number from \( \{1,2,3 \), \( -4,5\} \) is \( \alpha \times 5^{6} \) then \( \alpha \) is equal to
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