Can anyone help me solve those questions? Thank you. Question 2: A password is a

Question

Can anyone help me solve those questions? Thank you.

Question 2: A password is a string of ten characters, where each character is a lowercase letter, a digit, or one of the eight special characters a, S, &, and A password is called awesome, if it contains at least one digit or at least one special character. Determine the number of awesome passwords. Question 3: Determine the number of functions f 1, 2, 3, 4) {a, b, c, f(1) f(3) Question 4: Let n? 1 be an integer Assume that n is odd. Determine the number of bitstrings of length n that contain more 0's than 1's. Justify your answer in plain English and at most three sentences. Hint: Symmetry. Assume that n is even. Determine the number of bitstrings of length n in which the number of 0's is equal to the number of 1's. Determine the number of bitstrings of length n that contain strictly more 0's than 1's

Explanation / Answer

Answer: Total length of password = 10 characters

Awesome: If password contains atleast one digit or atleast one special character

Total possible passwords = (26+10+8)10 = 4410

Total possible passwords without digit = 3410                                              

Total possible passwords without special character = 3610                                                      

Total possible passwords without digit AND without special character = 2610                                          

Total possible passwords only lowercase = 2610

Total possible passwords only digit = 1010

Total possible passwords only special character= 810

Possible number of awesome passwords = 4410-3410-3610-2610-1010-810 = 2.14768E+16

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