Binomial Theorem 16

Probability Level 1

What is the coefficient of the $x^{3}y^{13}$ term in the polynomial expansion of $(x+y)^{16}?$

The answer is 560.

2 solutions

Andy Hayes
Dec 14, 2016

In order to achieve a product of $x^{3}y^{13},$ the " $x$ " in the binomial must be "chosen" 3 times out of 16. Thus, the coefficient of the $x^{3}y^{13}$ is equal to the number of combinations of 3 objects out of 16:

$\binom{16}{3}=\boxed{560}.$

For finding the best way of the solution ,we first take the question
(X^3 Y^13) .Divide the both terms for better clarity ˭˃ ((X^3) . (Y^13)) ˭˃ implementing in the given question ˭˃ (X.Y)^16 ˭˃ ((X) . (Y))^16 ˭˃ ((X)^3 . (Y)^13)

                                                        ˭˃ 16  C 13 .  (X)^3 . (Y)^13  
                                                           ˭˃560 .X^3.Y^3

Therefore ,the co-effficient of the X^3.Y^3 ˭˃ 560 . More doubts go to this link and watch last 20 mintues... https://www.youtube.com/watch?v=XPmrvRiTruw

Aswin rj - 6 months, 3 weeks ago

Raghul Rox Rox
Nov 22, 2020

By using binomial theorem, we will get (16/13)x^3 y^13. implementing this values as n=16 and k=13 in binomial factorial formula (16/13)= (16.15.14)/(3.2.1) =>16.5.7 => 560

Binomial Theorem 16

The answer is 560.

2 solutions

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