Understanding C(n,1) in Discrete Math: Solving the Mystery of C(n,1) = 1

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SUMMARY

The discussion clarifies the calculation of C(n,1) in discrete mathematics, confirming that C(n,1) represents "n choose 1." The formula for combinations, C(n,k) = n! / (k!(n-k)!), is applied to derive that C(n,1) equals n. This is established by substituting k with 1, leading to the conclusion that C(n,1) = n. The discussion emphasizes the straightforward nature of this calculation.

PREREQUISITES
  • Understanding of factorial notation (n!)
  • Familiarity with combinations and the binomial coefficient
  • Basic knowledge of discrete mathematics concepts
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the properties of combinations and permutations in discrete mathematics
  • Learn about the binomial theorem and its applications
  • Explore advanced topics in combinatorial mathematics
  • Practice solving problems involving C(n,k) for various values of n and k
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Students of discrete mathematics, educators teaching combinatorial concepts, and anyone looking to strengthen their understanding of combinations and factorials.

abbey gamble
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C(n,1) ...

I know that C(n,0) =1

But have no clue how to figure out C(n,1) :cry:
 
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By C(n,1) you mean n choose 1?

Do you know the definition of C(n,k)?
 
[tex]C(n,k) = \frac{n!}{k!\left(n-k\right)!}[/tex]
just use this to calculate C(n,1)
 

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