For \( r=0,1, \ldots, 10 \), let \( A_{r}, B_{r} \) and \( C_{r} \) denote, respectively, the co...
For \( r=0,1, \ldots, 10 \), let \( A_{r}, B_{r} \) and \( C_{r} \) denote, respectively, the coefficient of \( x^{r} \) in the expansions of \( (1+x)^{10},(1+x)^{20} \) and \( (1+x)^{30} \). Then - \( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-C_{10} A_{r}\right) \) is equal to
(a) \( B_{10}-C_{10} \)
(b) \( A_{10}\left(B_{10}^{2}-C_{10} \mathrm{~A}_{10}\right) \)
(c) 0
(d) \( C_{10}-B_{10} \)
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