Factorial Function and Permutations Quiz
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Factorial Function and Permutations Quiz

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Questions and Answers

What is the value of 4 factorial?

  • 20
  • 30
  • 24 (correct)
  • 25
  • In a race with 8 runners, how many different possible finishing orders are there?

  • 336
  • 56
  • 720
  • 5040 (correct)
  • What is the value of zero factorial?

  • 0
  • Undefined
  • 1 (correct)
  • -1
  • How do factorials relate to combinations and permutations?

    <p>Factorials are used to calculate both combinations and permutations</p> Signup and view all the answers

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

    <p>$1,000,000$</p> Signup and view all the answers

    Which mathematical concept is closely connected to factorial function?

    <p>Pascal's Triangle</p> Signup and view all the answers

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

    <p>1 - 0.5x^(-2)</p> Signup and view all the answers

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

    <p>1 - 2x^(0.5)</p> Signup and view all the answers

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

    <p>1 + 2x^(-3.5/3)</p> Signup and view all the answers

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

    <p>The constant term</p> Signup and view all the answers

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

    <p>To factor a and b out of the two terms within the bracket</p> Signup and view all the answers

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

    <p>(b/a)x^n + 1</p> Signup and view all the answers

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

    <p>To express it in the format of one plus a term</p> Signup and view all the answers

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

    <p>1 + 2x^(-1)</p> Signup and view all the answers

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

    <p>-3 + 6x^(-2)</p> Signup and view all the answers

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

    <p>1 + 2x^(-3.5/3)</p> Signup and view all the answers

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

    <p>(a + b)x^n</p> Signup and view all the answers

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

    Signup and view all the answers

    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.

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    Description

    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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