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Factorials quiz

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이 집합의 용어 (15)

  • What mathematical operation does the exclamation point represent when placed after a number or variable?
    It represents the factorial operation, which multiplies all whole numbers from the given number down to 1.
  • How do you calculate 4 factorial (4!)?
    Multiply 4 × 3 × 2 × 1, which equals 24.
  • What is the value of 1 factorial (1!)?
    1 factorial is equal to 1.
  • How is 2 factorial (2!) calculated?
    2 factorial is 2 × 1, which equals 2.
  • What is the value of 3 factorial (3!)?
    3 factorial is 3 × 2 × 1, which equals 6.
  • How do you calculate 5 factorial (5!)?
    Multiply 5 × 4 × 3 × 2 × 1, which equals 120.
  • What pattern can you observe in calculating consecutive factorials?
    Each factorial is the previous factorial multiplied by the new number.
  • How can you express n factorial (n!) in terms of the previous factorial?
    n factorial is n × (n-1) factorial.
  • What is the value of 6 factorial (6!)?
    6 factorial is 6 × 5 × 4 × 3 × 2 × 1, which equals 720.
  • How can you simplify 4 × 3 factorial?
    4 × 3 factorial is the same as 4 factorial, which equals 24.
  • How do you simplify 100 factorial divided by 99 factorial (100! / 99!)?
    100! / 99! simplifies to 100, since 100! = 100 × 99! and 99! cancels out.
  • What is the value of 0 factorial (0!)?
    0 factorial is defined as 1.
  • Why is 0 factorial (0!) equal to 1?
    By the factorial formula, 1! = 1 × 0!, and since 1! = 1, 0! must be 1.
  • In which areas of mathematics are factorials commonly used?
    Factorials are used in combinatorics, probability, sequences, and polynomial operations.
  • How does understanding factorials help in simplifying algebraic expressions?
    It allows you to break down and cancel terms, making calculations easier and more efficient.