A) 100
B) 120
C) 720
D) 1260
E) 1440
Correct Answer: D
Solution :
\[{{(bc+ca+ab)}^{9}}={{[bc+a(b+c)]}^{9}}\] \[\therefore \]Coefficient of \[{{a}^{5}}{{b}^{6}}{{c}^{7}}\] = coefficient of\[{{a}^{5}}{{b}^{6}}{{c}^{7}}\]in\[^{9}{{C}_{5}}\]in \[{{(bc)}^{4}}{{a}^{5}}{{(b+c)}^{5}}\] = coefficient of\[{{b}^{2}}{{c}^{3}}\]in \[^{9}{{C}_{5}}{{(b+c)}^{5}}\] \[{{=}^{9}}{{C}_{5}}{{\times }^{5}}{{C}_{2}}=\frac{9!}{5!\,\times 4!}\times \frac{5!}{3!\times 2!}\] \[=\frac{9\times 8\times 7\times 6\times 5}{3\times 2\times 1\times 2}=1260\]
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