Question

question 3 of 10
the coefficient of ( x^k y^{n - k} ) in the expansion of ( (x + y)^n ) equals ( dbinom{k}{n} ).

a. true

b. false

Explanation:

Step1: Recall binomial theorem

The binomial expansion of $(x+y)^n$ is $\sum_{k=0}^{n} \binom{n}{k}x^ky^{n-k}$, so the coefficient of $x^ky^{n-k}$ is $\binom{n}{k}$.

Step2: Compare with given statement

The given statement claims the coefficient is $\binom{k}{n}$, but $\binom{k}{n}=0$ when $k

Answer:

B. False