A password is a sequence of letters (a–z) and digits (0–9). Findthe number of passwords...

(a) There are 3 letters and 7 digits, and at most one ‘9’.

(b) There are 6 letters and 4 digits, and no digit occurs twice.

(c) No letters are used BUT the first four digits are not all the same AND the last four digits are not all the same, AND the 4th, 5th, 6th and 7 digits are not all the same.

Solutions

Expert Solution

a) P = P(with zero 9) + P(with one 9)

= 10C3(26)3(9)7 + 10C3(26)3(9)6 Answer

b) P = 10C6(26)6(10*9*8*7) Answer

(Here first we selected 6 places out of 10 for alphabets, then assigned alphabets to those places, then placed the four digits)

c) P = P( Making a password from digits) - P(Making a password from digits only, and first four are same, next four are same and the last four digits are same)

= (10)10 - (10)3 Answer

orchestra answered 1 year ago

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