Combination of Multiset 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. In the case of combination of Multiset, which allow repeated elements, combinations involve selecting subsets that may contain duplicates, depending on the multiplicity of elements in the multiset.

Explore the following Combination of Multiset examples to learn how to find different ways to choose items in various contexts.
Example 1: Combinations with Multiset of Fruits

• Problem: How many ways can 3 pieces of fruit be chosen from the multiset {Apple, Apple, Orange}?
• Solution: To calculate, consider all possible distributions of the fruits while respecting their frequencies. The possible combinations is: {Apple, Apple, Orange}.
• Answer: There is 1 way to choose the fruits.

Example 2: Combinations with Multiset of Letters

• Problem: How many ways can 3 letters be chosen from the multiset {A, A, B, B}?
• Solution: To calculate, consider all possible distributions of the letters while respecting their frequencies. The possible combinations are: {A, A, B}, {A, B, B}.
• Answer: There are 2 ways to choose the letters.

Example 3: Combinations with Multiset of Items

• Problem: How many ways can 2 items be chosen from the multiset {Red, Blue, Blue, Pink, Pink, Yellow}?
• Solution: To calculate, consider all possible distributions of the items while respecting their frequencies. The possible combinations are: {Red, Blue}, {Red, Pink}, {Red, Yellow}, {Blue, Pink}, {Blue, Yellow}, {Pink, Pink}, {Pink, Yellow}, {Blue, Blue}.
• Answer: There are 8 ways to choose 2 items from the multiset.

Engage in this Combination of Multiset 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 3 balls be chosen from 4 types of balls, where each type has an unlimited supply?
Ans 1: 20.
Que 2: How many ways can 4 letters be chosen from the multiset {A, A, B, B, C}?
Ans 2: 2.
Que 3: How many ways can 3 flowers be chosen from the multiset {Rose, Rose, Tulip}?
Ans 3: 1.
Que 4: How many ways can 2 items be chosen from the multiset {Red, Red, Blue, Blue, Green}?
Ans 4: 5.
Que 5: How many ways can 2 letters be chosen from the multiset {A, A, B, C, C}?
Ans 5: 5.