## 18 Questions

What is the value of 4 factorial?

24

In a race with 8 runners, how many different possible finishing orders are there?

5040

What is the value of zero factorial?

1

How do factorials relate to combinations and permutations?

Factorials are used to calculate both combinations and permutations

What is the maximum value that calculators can typically compute for factorials?

$1,000,000$

Which mathematical concept is closely connected to factorial function?

Pascal's Triangle

When dealing with the term 3 - 2x^(-2), what would be the binomial expansion after factoring out the constant term?

1 - 0.5x^(-2)

For the term 4 - 16x^(0.5), what is the binomial expansion after factoring out the constant term?

1 - 2x^(0.5)

When dealing with the term 9 + 18x^(-3.5), what is the binomial expansion after factoring out the constant term?

1 + 2x^(-3.5/3)

In the binomial expansion formula one plus ax, what does 'a' represent?

The constant term

What is the goal when dealing with a term like (a + b)x^n in binomial expansion?

To factor a and b out of the two terms within the bracket

What is the result of expanding 1 + (b/a)x^n in binomial expansion?

(b/a)x^n + 1

When dealing with the term (a + b)x^n, what is the goal in terms of its format?

To express it in the format of one plus a term

What is the result of factoring 2 out of the two terms in the term 2 + 4x^(-1)?

1 + 2x^(-1)

What is the binomial expansion of the term 3 - 2x^(-2) after factoring out 3?

-3 + 6x^(-2)

For the term 9 + 18x^(-3.5), what is the format after factoring out 9?

1 + 2x^(-3.5/3)

What is the result of expanding 1 + (b/a)x^n then multiplying it by the coefficient of a?

(a + b)x^n

What is the formula for binomial expansion when n is not a whole number?

## Study Notes

- Factorial function is written as a number followed by the symbol "!" and is used to calculate the number of arrangements or permutations of a given set of items.
- Factorial function is based on combinations and permutations, and stems from finding the number of different ways items can be arranged in a specific order.
- For example, in a race with five runners, there are 5 ways to choose the first place runner, 4 ways to choose the second place runner (after the first place runner has been chosen), and so on.
- The number of arrangements or permutations is the product of the number of choices for each position. For example, in a race with five runners, there are 5! (120) different possible finishing orders.
- Factorial function values for the first few numbers are: 1! = 1, 2! = 2, 3! = 6, 4! = 24, 5! = 120. Zero factorial is a special case and is defined as 1.
- Factorial function values increase quickly and calculators can only compute values up to a certain limit.
- Factorial function is connected to Pascal's Triangle and the nCr formula, which will be discussed next.

Test your knowledge of the factorial function, permutations, and combinations with this quiz. Learn about how the factorial function is used to calculate the number of arrangements or permutations of a given set of items, its connection to Pascal's Triangle, and the nCr formula.

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