Question
Question: The coefficient of x<sup>4</sup> in the expansion of (1 + x + x<sup>2</sup> + x<sup>3</sup>)<sup>11<...
The coefficient of x4 in the expansion of (1 + x + x2 + x3)11 is
A
990
B
605
C
303
D
330
Answer
990
Explanation
Solution
(1 + x + x2 + x3)11 = (1 + x)11 (1+ x2)11
= (1 + 11C1x + 11C2x2 + ...) (1+11C1x2 + 11C2x4+....)
Coefficient of x4 = 11C2.11C1+11C4+11C2
= 605 + 330 + 55
= 990