Understanding Zero Factorial

The video explains why zero factorial is equal to one through two justifications. The first justification uses a pattern approach, showing how dividing factorials by decreasing integers leads to zero factorial being one. The second justification involves permutations, explaining that zero factorial represents the number of ways to arrange zero items, which is one. These explanations help clarify the concept of zero factorial in mathematics.

What is the definition of n factorial for a non-negative integer?

• The sum of all positive integers less than or equal to n

• The division of all positive integers less than or equal to n

• The product of all positive integers less than or equal to n

• The difference of all positive integers less than or equal to n

How can we determine the value of zero factorial using a pattern?

• By multiplying the factorial of one by zero

• By subtracting one from the factorial of one

• By adding one to the factorial of one

• By dividing the factorial of one by one

What is the value of 5 factorial?

• 120

• 6

• 24

• 720

What is the value of 3 factorial?

• 720

• 6

• 24

• 120

What is the value of 2 factorial?

• 3

• 1

• 4

• 2

What is the value of 1 factorial?

• 3

• 2

• 1

• 0

How is zero factorial justified using permutations?

• There are no permutations possible with zero items

• There is one way to arrange zero items

• Zero factorial is undefined in permutations

• Zero factorial equals the number of items

What does a factorial represent in terms of permutations?

• The number of ways to subtract items

• The number of ways to add items

• The number of ways to arrange items

• The number of ways to divide items

How many permutations are there for three items?

• 3

• 6

• 12

• 9

Why is zero factorial equal to one?

• Because it is the sum of all integers

• Because it is the product of all integers

• Because it is defined that way

• Because it is the difference of all integers