Question 1

Which formula is used to calculate the number of combinations of $$n$$ objects taken $$r at a $$time?

Accepted Answer

$$\frac{n!}{r!(n-r)!}$$

Question 2

A medical research team needs to select 4 volunteers from a group of 10 for a clinical trial. How many different groups of 4 can be formed?

Accepted Answer

$$210$$

Question 3

Which of the following statements best describes a combination?

Accepted Answer

The selection of objects where order does not matter.

Question 4

If a chemistry lab has 7 different chemicals and wants to choose 3 for an experiment, how many possible combinations are there?

Accepted Answer

$$35$$

Question 5

Which of the following is the correct factorial formula for combinations?

Accepted Answer

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

Question 6

A committee of 5 is to be formed from 12 candidates. How many different committees are possible?

Accepted Answer

$$792$$

Question 7

Which scenario best illustrates the use of combinations rather than permutations?

Accepted Answer

Selecting a team of 3 from a group of 8.

Question 8

If $$n = 9$$ and $$r = 2$$, what is $$C(9, 2)$$?

Accepted Answer

$$45$$

Question 9

A school is forming a group of 6 students from a class of 15. How many different groups can be formed?

Accepted Answer

$$5005$$

Question 10

Which of the following is NOT a property of combinations?

Accepted Answer

Order of selection matters.

Question 11

A biologist wants to select 2 species out of 8 for a study. How many ways can this be done?

Accepted Answer

$$56$$

Question 12

If $$C(n, r) = 10$$ and $$n = 5$$, what is the value of $$r$$?

Accepted Answer

$$3$$

Question 13

A pharmacist needs to choose 4 medicines from a shelf of 9. How many different selections are possible?

Accepted Answer

$$126$$

Question 14

Which of the following expressions represents the number of ways to choose 0 objects from $$n$$ objects?

Accepted Answer

$$1$$

Question 15

A team of 3 engineers is to be selected from 7 candidates. How many different teams can be formed?

Accepted Answer

$$35$$

Combinations and the Factorial Formula in College Algebra

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