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7.Binomial Theorem
normal
Sum of co-efficients of terms of degree $m$ in the expansion of $(1 + x)^n(1 + y)^n(1 + z)^n$ is
A
${\left( {{}^n{C_m}} \right)^3}$
B
$3\left( {{}^n{C_m}} \right)$
C
$\left( {{}^n{C_{3m}}} \right)$
D
$\left( {{}^{3n}{C_m}} \right)$
Solution
General term $ = \sum {\left( {^n{C_r}} \right)} \left( {^n{C_s}} \right)\left( {^n{C_t}} \right){x^r}{y^s}{z^t}$
Where $r+s+t=m.$
Sun of coefficient $=$ No. of ways of chossing a total of $m$ balls out of $n$ black, $n$ white and $n$ green balls.
$ = {\,^{3n}}{C_m}.$
Standard 11
Mathematics
