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The coefficient of $a^{10} b^7 c^3$ in the expansion of $(b c+c a+a b)^{10}$ is
Option: 1
$150$

Option: 2
$120$

Option: 3
$100$

Option: 4
$180$

Answers (1)

best_answer

The general term in the expansion of $(b c+c a+a b)^{10}$ is

$\frac{10 !}{r ! s ! t !}(b c)^\gamma(c a)^s(a b)^t=\frac{10 !}{r ! s ! t !} a^{t+s} b^{r+t} c^{r+s}$

where $r + s + t = 10$

For coefficient of $a^{10} b^7 c^3,$ we set $t+s=10, r+t=7, r+s=3 \text {. }$

Since $r + s + t = 10,$ we get $r=0, s=3, t=7$

Thus, on solving the coefficient of $a^{10} b^7 c^3$ in the expansion is 120

$\frac{10 !}{0 ! 3 ! 7 !}=\frac{10 \times 9 \times 8}{3 \times 2}=120$

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Ritika Harsh

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