JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 21

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 S whose at least one character is a number from {1, 2, 3, 4, 5} is $\alpha\times5^6$, then $\alpha$ is equal to ______.