need complete answer plxx 2. A computer password consists of ten non-repeating c

Question

need complete answer plxx

2. A computer password consists of ten non-repeating characters. How many different passwords are possible if each character may be any lowercase letter or digit? How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? Calculate the number of passwords in parts (a) and (b), if characters can be repeated. a. b. c. 3. In a manufacturing process, 30 parts are randomly selected every day for quality control. Tvpically, 20

Explanation / Answer

(a) Total = 10 non-repeating characters: any lowercase letter or digits

Number of lowercase letters = 26

Number of digits = 10

So,

Number of different passwords = 36 X 35 X 34 X 33 X 32 X 31 X 30 X 29 X 28 X 27 = 922,393,263,052,800

(b)

Number of passwords with no digit = 26 X 25 X 24 X 23 X 22 X 21 X 20 X 19 X 18 X 17 = 19,275,223,968,000

So,

Number of passwords with al least one character must be a digit = 922,393,263,052,800 - 19,275,223,968,000 = 908,118,039,084,800

(c)

If characters can be repeated:
(i) Number of different passwords = 3610= 3,656,158,440,062,976

(ii) With no digit = 2610 = 141,167,095,653,376

So,

Number of passwords with at least one digit = 3,514,991,344,409,600

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