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Word Combination Calculator

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Answer: Ways to select 3 letters from the word WORD is 4.
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Total Elements (Individuals) [4] 𝒊
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Selected Elements (All on same stage) [3] 𝒊
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Combination Selector 𝒊
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Word Combination

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. Word combination refers to selecting characters from a word, where the combination creates subsets of characters without regard to the sequence of those characters, forming possible groupings of the letters.
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Word Combination Formula

In cases where we want to find how many combinations can be made from a word to form a subset of letters, we use the word combination formula:
C = ( n + r - 1 ) ! r ! ⋅ ( n - 1 ) !
C = Combination | n = total number of elements | r = number of elements to choose

Word Combination Examples

Explore the following Word Combination examples to learn how to find different ways to choose items in various contexts.
Example 1: Combinations of Letters from GRAPE
  • Problem: How many ways can 2 letters be chosen from the word GRAPE?
  • Solution: The word GRAPE contains the letters G, R, A, P, E, each appearing once. The number of combinations of 2 letters from these 5 unique letters is calculated as C(5, 2) = 10.
  • Answer: There are 10 ways to choose the letters.
Example 2: Combinations of Letters from BEE
  • Problem: How many ways can we choose 2 letters from the word BEE?
  • Solution: To calculate, consider all possible distributions of the letters while respecting their frequencies. The possible combinations are:{E, E}, {B, E}.
  • Answer: There are 2 ways to choose the letters.
Example 3: Combinations of Letters from MOON
  • Problem: How many ways can we choose 3 letters from the word MOON?
  • Solution:To calculate, consider all possible distributions of the letters while respecting their frequencies. The possible combinations are: {O, O, M}, {O, O, N}, {M, O, N}
  • Answer: There are 3 ways to choose the letters.

Word Combination Exercise

Engage in this Word Combination 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 2 letters be chosen from the word APPLE?
Ans 1: 7.
Que 2: How many ways can 3 letters be selected from the word BANANA?
Ans 2: 6.
Que 3: How many ways can 2 letters be chosen from the word MATH?
Ans 3: 6.
Que 4: How many ways can 4 letters be chosen from the word GARDEN?
Ans 4: 15.
Que 5: How many ways can 3 letters be chosen from the word CAT?
Ans 5: 1.

Word Combination Calculator FAQ

How are word combinations used in real life?
Word combinations are used in various contexts such as creating passwords, forming abbreviations, generating anagrams, and in word games.
Can word combinations include non-alphabetic characters?
Yes, combinations can include non-alphabetic characters if they are part of the original set of characters in the word.
Can you provide an example of word combinations?
For example, from the word CAT, the combinations of two letters are: CA, CT, and AT. The order does not matter.
What if the letters in the word have repetitions?
If a word contains repeated letters, the number of unique combinations can be calculated using the formula that considers the frequency of each letter.
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