Question

question 4 of 10
what is the coefficient of ( x^5y^5 ) in the expansion of ( (x + y)^{10} )?

a. 1

b. 5

c. 252

d. it does not exist.

Explanation:

Step1: Apply binomial theorem

The coefficient of $x^k y^{n-k}$ in $(x+y)^n$ is $\binom{n}{k}$. Here $n=10$, $k=5$.

Step2: Calculate combination

$\binom{10}{5} = \frac{10!}{5!5!} = \frac{10×9×8×7×6}{5×4×3×2×1} = 252$.

Answer:

C. 252