Customers who register to bank online with Cambio Bank are issued a randomly gen

Question

Customers who register to bank online with Cambio Bank are issued a randomly generated password that is 5 characters long, each of which can be one of the 26 lowercase letters of the alphabet, one of the single digit numbers between 0 and 9, or one of these special characters: @, #, $, %. What is the probability that one of these passwords does NOT contain any repeated characters?

The answer is 0.771. I cannot figure out how this is the correct answer though. Please show problem with all work and the formula used

Explanation / Answer

Total number of choices for each character = 26 + 10 + 4 = 40

So,

Total number of passwords of 5 digits possible = 405 = 102400000

Now,

Number of passwords which doesn't contain any repeated characters = 40*39*38*37*36 = 78960960

Hence,

P(Password does NOT contain any repeated characters)

= 78960960 / 102400000

= 0.771

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