Combination of Set Calculator

Combination is a mathematical concept that refers to the selection of elements from a collection, where the order of the elements does not affect the result. A combination of set involves choosing a subset of distinct elements from a larger set, with no element being selected more than once. The size of the subset is typically smaller than or equal to the size of the original set.

Explore the following Combination of Set examples to learn how to find different ways to choose items in various contexts.
Example 1: Combinations of a Set of Numbers

• Problem: How many ways can a subset of 2 elements be chosen from the set {1, 2, 3, 4}?
• Solution: Using combination formula: 4! / [2! × (4 - 2)!] = 6.
• Answer: There are 6 ways to choose the subset.

Example 2: Combinations of a Set of Letters

• Problem: How many ways can a subset of 3 letters be chosen from the set {A, B, C, D, E}?
• Solution: Using combination formula: 5! / [3! × (5 - 3)!] = 10.
• Answer: There are 10 ways to choose the subset.

Example 3: Combinations of a Set of Colors

• Problem: How many ways can a subset of 4 colors be selected from the set {Red, Blue, Green, Yellow, Black, White}?
• Solution: Using combination formula: 6! / [4! × (6 - 4)!] = 15.
• Answer: There are 15 ways to choose the subset.

Engage in this Combination of Set exercise to explore the concept of combinations through practical questions. Challenge your skills in determining how to select items.
Que 1: How many ways can a subset of 2 elements be chosen from the set {A, B, C, D}?
Ans 1: 6.
Que 2: How many ways can a subset of 3 elements be selected from the set {1, 2, 3, 4, 5}?
Ans 2: 10.
Que 3: How many ways can a subset of 4 elements be chosen from the set {P, Q, R, S, T, U}?
Ans 3: 15.
Que 4: How many ways can a subset of 1 element be selected from the set {X, Y, Z}?
Ans 4: 3.
Que 5: How many ways can a subset of 3 elements be chosen from the set {a, b, c, d, e, f}?
Ans 5: 20.