4. Probability

Counting

4. Probability

Counting

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Multiple Choice

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?

$2197$

$1716$

$13$

$6$

Verified step by step guidance

Identify the total number of members available for selection, which is 13.

Understand that the positions of president, vice president, and treasurer are distinct, meaning the order of selection matters.

Use the concept of permutations to determine the number of ways to fill these positions. The formula for permutations is given by:

P (n, r) = \frac{n!}{(n - r)!}

, where n is the total number of items to choose from, and r is the number of items to choose.

Substitute the values into the permutation formula:

P (13, 3) = \frac{13!}{(13 - 3)!}

Calculate the factorial values and simplify the expression to find the number of ways to fill the positions.

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In Exercises 41-44, perform the indicated calculation.

42. 8P6

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Textbook Question

In Exercises 41-44, perform the indicated calculation.

44. (5C3)/(10C3)

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Textbook Question

4. The table on the left shows the secondary school student enrollment levels (in thousands by grade) in Oklahoma and Texas schools in a recent year. (Source: U.S. Nation

for Education Statistics)

A student in one of the indicated grades and states is randomly selected. Find the probability of selecting a student who

d. is enrolled in Texas, given that the student is in twelfth grade.

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Textbook Question

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?

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Multiple Choice

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?

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