Question

what is the coefficient of x^5y^5 in the expansion of (x+y)^10

Answer 1

Answer:

252

Step-by-step explanation:

We know the binomial expansion of  

$(a + x)^{n} = a^{n} + C_{1}a^{(n - 1)} x + C_{2} a^{(n - 2)} x^{2} + ........ + C_{r} a^{(n - r)} x^{r} + ........ + x^{n}$

Therefore, in the binomial expansion of $(x + y)^{10}$ the term with $x^{5}y^{5}$ expression will be there when r = 5

Hence, the term will be $^{10}C_{5} x^{5} y^{5}$.

Therefore, the coefficient of $x^{5}y^{5}$ will be

$^{10}C_{5} = \frac{10!}{5! \times 5!} = 252$ (Answer)