1. Count the number of binary strings of length 10 subject to each of the following...

  

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1. Count the number of binary strings of length 10 subject to each of the following restrictions. (a) The string has at least one 1. (b) The string has at least one 1 and at least one 0. 2. How many different passwords are there that contain only digits and lower-case letters when the password length is 6 and the password must contain at least one digit and at least one letter. 3. Count the number of strings of length 9 over the alphabet {a, b, c} when the string contains at least 8 consecutive a's. 4. How many ways are there to permute the letters in each of the following words? PROBLEM 1. Count the number of binary strings of length 10 subject to each of the following restrictions. (a) The string has at least one 1. (b) The string has at least one 1 and at least one 0. 2. How many different passwords are there that contain only digits and lower-case letters when the password length is 6 and the password must contain at least one digit and at least one letter. 3. Count the number of strings of length 9 over the alphabet {a, b, c} when the string contains at least 8 consecutive a's. 4. How many ways are there to permute the letters in each of the following words? PROBLEM

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