Combinations and Permutations Concepts

This video tutorial on the TechMath channel explains how to calculate combinations and permutations. It begins with an introduction to the concepts, highlighting the difference between combinations and permutations, where order matters in permutations but not in combinations. The tutorial uses examples, such as selecting books and forming committees, to demonstrate how to calculate the number of combinations and permutations. It also introduces the combinations rule and provides step-by-step examples to solidify understanding.

What is the main difference between combinations and permutations?

• Combinations consider order, permutations do not.

• Permutations consider order, combinations do not.

• Both consider order.

• Neither consider order.

In the context of combinations, why does the order of selection not matter?

• Because the items are always in numerical order.

• Because the items are identical.

• Because the items are always in alphabetical order.

• Because the focus is on the group, not the sequence.

How many different ways can you select 3 books from a set of 5?

• 10

• 20

• 30

• 60

What is the first step in calculating permutations?

• Multiply the number of choices for each position.

• Divide by the factorial of the number of items.

• Subtract the number of items from the total.

• Add the number of items together.

How do you adjust a permutation calculation to find combinations?

• Add the factorial of the number of items.

• Multiply by the factorial of the number of items.

• Divide by the factorial of the number of items.

• Subtract the factorial of the number of items.

What does 'n factorial' represent in the combinations formula?

• The sum of all numbers up to n.

• The product of all numbers up to n.

• The division of all numbers up to n.

• The difference of all numbers up to n.

In the combinations formula, what does 'r factorial' represent?

• The number of ways to arrange r items.

• The number of ways to add r items.

• The number of ways to divide r items.

• The number of ways to select r items.

How many different ways can you select 4 people from a group of 10?

• 360

• 210

• 504

• 120

What is the purpose of dividing by 'r factorial' in the combinations formula?

• To account for the different arrangements of selected items.

• To account for the total number of items.

• To account for the repetition of items.

• To account for the order of selection.

How many different ways can you select 5 players from a group of 8?

• 168

• 70

• 112

• 56