Gr 12 Mathematics: Ch 9.4 Factorial Notation

What is the value of 0! in factorial notation?

Infinity

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1 (correct)

0

What is the total number of possible arrangements of n different objects?

n! (correct)

2 × n

(n - 1)!

n × (n - 1) × (n - 2) × ... × 3 × 2 × 1

What is the product of all positive integers up to n represented by?

n × n

n × (n - 1) × (n - 2) × ... × 3 × 2

n! (correct)

(n - 1)!

What is true about the factorial of any non-negative integer n?

It is the product of all positive integers less than or equal to n Signup and view all the answers

What is the value of n! / (n-1)! for any positive integer n?

n Signup and view all the answers

What is a use of the factorial of n?

To simplify expressions involving permutations and combinations Signup and view all the answers

What does the notation n! (read as 'n factorial') represent?

The product of all positive integers up to n Signup and view all the answers

In which type of problem is factorial notation commonly used?

Counting problems Signup and view all the answers

What is a property of the factorial of a positive integer n?

It can be used to simplify expressions involving permutations and combinations Signup and view all the answers

How can factorial notation be used in permutation and combination problems?

To simplify expressions involving permutations and combinations Signup and view all the answers

What is a characteristic of the way factorial notation can be expanded and simplified?

It depends on the context of the problem Signup and view all the answers

What is true about the relationship between n! and (n-1)!?

n! can be divided by (n-1)! Signup and view all the answers

Which of the following is a consequence of the outcome of the first event reducing the number of possible outcomes for the second event?

Factorial notation is used to represent the product of all positive integers up to a certain number Signup and view all the answers

What is a benefit of using factorial notation in permutation and combination problems?

It can be used to simplify expressions involving permutations and combinations Signup and view all the answers

What is the relationship between $n!$ and $(n-1)!$?

$n! = (n-1)! imes n$ Signup and view all the answers

What is the primary use of factorial notation in counting problems?

To represent the product of all positive integers up to a certain number Signup and view all the answers

What is a common situation where factorial notation is used?

When the outcome of the first event reduces the number of possible outcomes for the second event Signup and view all the answers

What is true about expanding and simplifying factorial notation?

It can be expanded and simplified in various ways depending on the context Signup and view all the answers