A student formed a club at their school. They have 13 members, and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?

5. Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total.

a. What is the theoretical probability of each total from 1 to 11?

b. Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a).

Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.

62. Find the probability of being dealt three of a kind (the other two cards are different from each other).

In Exercises 41-44, perform the indicated calculation.

42. 8P6

7. There are 16 students giving final presentations in your history course.

b. Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on

the same unit are indistinguishable from each other?

Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?

Evaluate the given expression. $_9P_4$

You want to arrange the books on your bookshelf by color. How many different ways could you arrange 12 books if 4 of them have a blue cover, 3 are yellow, and 5 are white?

How many ways are there to arrange the letters in the word CALCULUS?