Help Each character in a password is either a digit \([0 - 9]\) or a lowercase letter \([a - z]\). How many valid passwords are there with the given restriction(s)?- Length is 17.- No character repeats.- Must contain: \(a\).Example: \(P(11, 4) * P(4, 3)\)Write permutations as: \(P(n, k)\)

We have to find how many valid passwords are there with the given restriction(s). The length of the password must be 17 characters, and no character should be repeated.The characters that must be included in the password is a. The number of characters remaining in the password = 17−1=16All these 16 characters must be distinct, and also different from a. Explanation:These 16 characters can either be a digit or a lowercase letter except a.The remaining characters can be chosen from 10 + 25 = 35 characters.Explanation:As a cannot be chosen, the letters left that can be used = 26−1=25The number of ways to choose 25 characters from 35 = C(35,25)Explanation:C(n,k) represents the number of different ways you can choose k items from a set of n items without regard to the order in which they are chosen.It is given as = 183579396After all the characters have been chosen, the characters in the password can be rearranged in 17! ways.Explanation:The number of permutations of n items is n!.So, the number of ways to to arrange n characters is n!.Hence, total number of valid passwords = 183579396 × 17!Explanation:The factorial of a number is n! = n(n−1)(n−2)×…×3×2×1 i.e. it is the product of all numbers from 1 to n.Therefore, The total number of valid passwords = 183579396 × 17!