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Tree diagram, probability in card selection, math instructors

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2. A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 1, 3, or 5. Repetition of digits is NOT permitted. Each letter must be an A, B or C.

- Use the counting principle to determine the number of points in the sample space.
- Construct a tree diagram to represent this situation
- List the sample space.
- Determine the exact probability of creating a mini license plate with a C. Give solution exactly in reduced fraction form.

4. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

- a three given the card is a not a face card.
- a four, given that the card is not a diamond.
- a Jack given the card is not a face card.

Show step by step work. Give all solutions exactly in reduced fraction form.

5. In how many ways can 10 instructors be assigned to ten sections of a course in mathematics

6. In how many different ways can the top eight new indie bands be ranked on a top eight list? The top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?

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Tree diagrams, probability in card selection and math instructors are examined.

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2. A mini license plate for a toy car must consist of three numbers followed by a letter. Each number must be a 1, 3, or 5. Repetition of digits is NOT permitted. Each letter must be an A, B or C.
• Use the counting principle to determine the number of points in the sample space.
• Construct a tree diagram to represent this situation
• List the sample space.
• Determine the exact probability of creating a mini license plate with a C. Give solution exactly in reduced fraction form.

(a) The ...

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