Understanding Subsets and Combinatorics

The video tutorial explains how to calculate the number of subsets of a set with specific cardinalities using combinations. It covers subsets of cardinality 5, subsets containing specific elements, subsets with at least one odd number, and subsets with exactly one even number. The tutorial uses set S with elements 1 to 8 as an example and demonstrates the calculations step-by-step.

How many subsets of a set with 8 elements can be formed with exactly 5 elements?

• 70

• 28

• 120

• 56

What is the formula used to calculate the number of subsets of a set with a specific cardinality?

• k choose n

• n + k

• n choose k

• n^k

If a subset must include the elements 2, 3, and 5, how many additional elements are needed to form a subset of cardinality 5?

• 2

• 1

• 3

• 4

How many ways can you choose 2 elements from a set of 5 elements?

• 10

• 20

• 15

• 5

What is the number of subsets of cardinality 5 that include the elements 2, 3, and 5?

• 5

• 10

• 15

• 20

How many odd numbers are there in the set S?

• 2

• 4

• 5

• 3

Why must a subset of cardinality 5 from set S contain at least one odd number?

• Because there are more odd numbers than even numbers

• Because there are only 4 even numbers in set S

• Because odd numbers are required

• Because subsets must be balanced

How many even numbers are there in set S?

• 3

• 5

• 4

• 2

How many subsets of cardinality 5 contain exactly one even number?

• 2

• 5

• 3

• 4

What is the number of ways to choose 4 odd numbers from a set of 4 odd numbers?

• 4

• 3

• 2

• 1