Question

In the expansion of $(a+b+c{)}^{10}$

• A. total number of terms is $66$
• B. coefficient of $a^8$ bc is $90$
• C. coefficient of $a^4{b}^5{c}^3$ is $0$
• D. $none$ $of$ $these$

Answer 1

The correct option is A total number of terms is $66$

Number of terms in the given expansion is nothing but the non-negative integral solutions of the equation:

$a+b+c=10$

Total number of non-negative integral solutions

$\Rightarrow$ ${}^{(10+3-1)}{C}_{(3-1)}={}^{12}{C}_2$

$=\frac{12!}{(12-2)!2!}$

$=\frac{12!}{10!2!}$

$=\frac{12\times 11\times 10!}{10!\times 2\times 1}$

$=6\times 11$

$=66$

$\therefore$ Total number of terms is $66$