find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11

Dear Student,
Please find below the solution to the asked query:

As, 1+x+x2+x311= 11+x+x21+x11= 1+x1+x211= 1+x111+x211=1+C111x+C211x2+C311x3+C411x4+C511x5+...1+C111x2+C211x4+C311x6...Since, the coefficient of x4 can be found when 1 is multiplied with C211x4 or C211x2 with C111x2 or C411x4 with 1.So, the coefficient of x4=1×C211+C211×C111+C411×1                                         =1×11!2!×9!+11!2!×9!×11!1!×10!+11!4!×7!×1                                         =11×102+11×102×11+11×10×9×84×3×2                                         =11×102×12+11×10×3                                         =11×10×6+11×10×3                                         =11×10×9                                         =990

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

  • -1
What are you looking for?