Intermediate
Discrete Mathematics & Math
Q75 / 100
What is the value of C(n,0) + C(n,1) + C(n,2) + ... + C(n,n)?
Correct! Well done.
Incorrect.
The correct answer is B) 2ⁿ
B
Correct Answer
2ⁿ
Explanation
By the Binomial Theorem, setting x=y=1 in (x+y)ⁿ = Σ C(n,k) xᵏ y^(n-k) gives Σ C(n,k) = 2ⁿ. This counts all subsets of an n-element set, since C(n,k) counts the k-element subsets and there are 2ⁿ subsets total.
Progress
75/100