Factorials and Their Applications

The video tutorial explores the concept of factorials, starting with a basic introduction and moving on to real-life applications, permutations, and the significance of zero factorial. It delves into the role of factorials in time systems and highlights unique properties of large factorials. The tutorial also covers mutant variations like primordials and hyper factorials, and introduces an approximation formula and the gamma function. The session concludes with a brief look at future topics.

What does the exclamation point symbolize in mathematics?

• Division

• Subtraction

• Factorial

• Addition

How many ways can you arrange three distinct items?

• 6

• 3

• 9

• 12

If you have five piano notes, how many different sequences can you play them in?

• 150

• 60

• 100

• 120

What is the factorial of 7?

• 362880

• 5040

• 40320

• 720

How many different ways can a deck of 52 cards be shuffled?

• 26 factorial

• 52

• 52 factorial

• 104 factorial

What is the factorial of zero?

• 0

• 1

• Undefined

• 10

Which factorial is the first not divisible by the sum of its digits?

• 432 factorial

• 120

• 5040

• 720

In base 21, which factorial is the first not divisible by the sum of its digits?

• 1899 factorial

• 720 factorial

• 1900 factorial

• 432 factorial

What is a primordial?

• A product of prime numbers up to a certain number

• A factorial of odd numbers

• A factorial of even numbers

• A factorial of all numbers

What is a double factorial?

• A factorial squared

• A factorial multiplied by two

• A factorial of even or odd numbers only

• A factorial of factorials