a randomly generated password contains four characters. each of the four characters is either a lowercase…

a randomly generated password contains four characters. each of the four characters is either a lowercase letter or a digit from 0 - 9. each character in the password cannot be used more than once. what is the approximate probability that exactly one of the four characters will be a number? 1% 11% 28% 44%

a randomly generated password contains four characters. each of the four characters is either a lowercase letter or a digit from 0 - 9. each character in the password cannot be used more than once. what is the approximate probability that exactly one of the four characters will be a number? 1% 11% 28% 44%

Answer

Answer:

44%

Explanation:

Step1: Calculate total number of possible passwords

There are 26 lowercase letters and 10 digits, so 36 total characters. Using permutations (P(n,r)=\frac{n!}{(n - r)!}), with (n = 36) and (r=4), the total number of 4 - character non - repeating passwords is (P(36,4)=\frac{36!}{(36 - 4)!}=36\times35\times34\times33=1413720).

Step2: Calculate number of passwords with exactly 1 number

First, choose the position for the number in (C(4,1)=\frac{4!}{1!(4 - 1)!}=4) ways. Then choose the number in 10 ways and the 3 non - number (lowercase letter) characters from 26 letters in (P(26,3)=\frac{26!}{(26 - 3)!}=26\times25\times24) ways. The number of passwords with exactly 1 number is (4\times10\times26\times25\times24 = 624000).

Step3: Calculate the probability

The probability (P=\frac{624000}{1413720}\approx0.44) or 44%.