1. Tardigrade
  2. Question
  3. Mathematics
  4. The coefficient of x7 in the expansion of (1-x-x2+x3)6 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The coefficient of $x^{7}$ in the expansion of $\left(1-x-x^{2}+x^{3}\right)^{6}$ is

AIEEEAIEEE 2011

Solution:

We have $\left(1-x-x^{2}+x^{3}\right)^{6}=(1-x)^{6}\left(1-x^{2}\right)^{6}$
coefficient of $x^{7}$ in
$\left(1-x-x^{2}+x^{3}\right)^{6}={ }^{6} C_{1} \cdot{ }^{6} C_{3}-{ }^{6} C_{3} \cdot{ }^{6} C_{2}+{ }^{6} C_{5} \cdot{ }^{6} C_{1} $
$=6 \times 20-20 \times 15+6 \times 6 $
$=-144$