3 Questions- Probability

1.What is the probability that a five-card poker hand contains five distinct

ranks? Justify your answer.

2. (10 points) Six families, numbered 1 through 6, meet once per month to have dinner

together at one of their six homes. Each month, a single six-sided die is rolled to

determine which family will host that month. What is the probability that over the next

12 months, every family will have hosted dinner at least once? Justify your answer.

3. (10 points) There are 95 possible password characters: 52 letters, 10 digits, and 33

special characters. A valid password must contain at least one letter, at least one digit,

and at least one special character. How many valid 8-character passwords are there?

Justify your answer.

Show work for all the 3 questions for full credit

Thanks 🙂