3rd Quarterly Exam Grade 10

Which of the following problems can be solved using counting techniques?

• What is the equation of the line passing through two given points in a coordinate plane?

• What is the derivative of a given function at a given point?

• How many ways are there to arrange 5 books on a bookshelf?

• What is the integral of a given function over a given interval?

How many ways can one choose a main course and a side dish from four choices of main courses and five choices of side dishes?

• 9

• 10

• 15

• 20

In how many ways can the letters of the word MATH be arranged?

• 4

• 12

• 24

• 48

Which one is equivalent to 5!?

• 5 × 1

• 5 × 4 × 2

• 5 × 4

• 5 × 4 × 3 × 2 × 1

1Which expression is equivalent to 4P4?

• 4 × 4

• 3 × 4

• 4 × 4 × 3 × 2 × 1

• 4 × 3 × 2 × 1

A group of 6 women and 9 men must select a six-person committee. How many committees are possible if each committee must consist of at most 4 women?

• 104

• 540

• 1,680

• 4,866

A new model of a car is available in five exterior colors, four interior colors, and two interior styles. How many versions of car are available for order?

• 20

• 40

• 80

• 120

A bookshelf has n different Algebra books and three different Geometry books. If there are 5,040 ways to arrange the books on the shelf, how many Algebra books are on the bookshelf?

• 4

• 5

• 6

• 7

Find the number of different arrangements of the letters of the word HONESTY if:

all seven letters are used.

•   300

• 360

• 3,600

• 5,040

Find the number of different arrangements of the letters of the word HONESTY if:

only two letters are taken at a time.

• 30

• 42

• 64

• 80