Factorials, Permutations, and Combinations

This video tutorial covers permutations and probability, starting with the basics of permutations and factorials. It explains how to calculate permutations, including those with restrictions and repeated elements. The tutorial also demonstrates how permutations are used in probability calculations, providing examples such as arranging news stories, creating license plates, and generating codes.

What is a permutation?

• A method to calculate probability

• A way to arrange objects in a specific order

• A way to count objects

• A type of mathematical operation

How many ways can the letters X, Y, and Z be arranged?

• 12

• 3

• 6

• 9

What does the symbol 'n!' represent in permutations?

• The division of n by 2

• The difference between n and 1

• The product of all positive integers up to n

• The sum of n numbers

How is 8 factorial (8!) calculated?

• 8 + 7 + 6

• 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

• 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

• 8 x 7 x 6

If a TV station has 8 news stories, how many different ways can they be arranged?

• 8

• 40,320

• 336

• 5,040

What is the formula for permutations of n objects taken r at a time?

• n! / (n-r)!

• n! / r!

• n! + r!

• n! x r!

How many ways can 3 stories be selected from 8?

• 336

• 56

• 720

• 1,680

What is the permutation of 50 people receiving 4 prizes?

• 50 x 49 x 48 x 47

• 50 x 49 x 48

• 50 x 49

• 50

How do you calculate permutations with repeated elements?

• n! - (x1! x x2! x ...)

• n! / (x1! x x2! x ...)

• n! x (x1! x x2! x ...)

• n! + (x1! x x2! x ...)

How many distinguishable permutations are there for the word 'SOCCER'?

• 60

• 180

• 360

• 720