Track / Stage 4 / 26 of 340 #286 of 2000

(3) The coefficient of $a b c^{2}$ in the expansion of $(a+2 b-3 c)^{4}$ is ( )
(A) 208
(B) 216
(C) 217
(D) 218

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Official solutions — 2

Solution 1

3. $\mathrm{B}$

Solution 2

3. B.

According to the problem, the coefficient of $a b c^{2}$ is $C_{4}^{2}(-3)^{2} C_{2}^{1} \times 2 \times 1=216$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.