Combinatorics Calculator

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Example

Created on 2024-06-20Asked by Ethan Adams (Solvelet student)

Find the number of ways to choose 3 elements from a set of 8 elements.

Solution

Step 1: Identify the formula for combinations:

\binom{n}{r} = \frac{n!}{r!(n-r)!}.

Step 2: Substitute

n = 8

and

r = 3

\binom{8}{3} = \frac{8!}{3!(8-3)!} = \frac{8!}{3! \cdot 5!}.

Step 3: Simplify the factorials:

\frac{8!}{3! \cdot 5!} = \frac{8 \cdot 7 \cdot 6 \cdot 5!}{3! \cdot 5!} = \frac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56.

Step 4: Conclusion. The number of ways to choose 3 elements from a set of 8 elements is 56. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ella Moore on Solvelet

1. How many ways are there to arrange the letters of the word 'COMBINATORICS'?,2. In how many ways can a committee of 3 people be selected from a group of 10?,

DefinitionCombinatorics: a field of math mainly focused on counting, arranging, and choosing objects disregarding their order or structure. Covers permutations, combinations, combinatorial identities, and principles of counting. As such, combinatorics is widely used in computer science, cryptography, probability theory, and optimization. It provides methods for analyzing discrete structures and problem-solving with finite sets and arrays. Example: Combinatorial methods in cryptography are employed in the study of encryption algorithms to determine the maximum number of unique keys and the ease of breaking the encryption.

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