2. A password has to use the following format: LDDDDLLL, where L can be any of the upper case letters in the alphabet, and D can be any digit including 0. None of the digits or letters can repeat. a. What is the probability that a random password uses only vowels (A,E,I,O,U) and odd numbers (1,3,5,7,9)? Show work but do not evaluate. b. What is the probability that the password spells the word "LOVE?" Show work but do not evaluate.

Consider a binary code with 6 bits (0 or 1) in each code word. An example of a code word is 010010. How many different code words are there? b. How many code words have exactly three O's? In each code word a bit is a 0 with probability 0.8, independent of any other bit, what is the а. С. probability of observing the code 001111. d. What is the probability that the code word will contain exactly three zeros (Hint: The way that you would read this statement is the P[observing exactly three zeros] = P[000111] + P[100011] + as you can see there are so many ways you could observe 3 zeros in a code, use the %3D etc combinatorics principle to help you find the probability in this question )

Five cards are selected out of 52. In how many different ways can this be done if: they contain at least 4 clubs?

Three cards are drawn from a s a. If each card is replaced b If there is no replaceme

A password has to use the following format: LDDDDLLL, where L can be any of the upper case letters in the alphabet, and D can be any digit including 0. None of the digits or letters can repeat. a. What is the probability that a random password uses only vowels (A,E,I,O,U) and odd numbers (1,3,5,7,9)? Show work but do not evaluate. b. What is the probability that the password spells the word "MATH?" Show work but do not evaluate.

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