(Solved): 1. (a) Use the binomial theorem to find the sum \( \sum_{k=1}^{10}\left(\begin{array}{c}10 \\ k\en ...

1. (a) Use the binomial theorem to find the sum \( \sum_{k=1}^{10}\left(\begin{array}{c}10 \\ k\end{array}\right) 3^{10-k} \). Hint: \( 3^{10-k}=1^{k} 3^{10-k} \) for any \( k \). (b) Use the multinomial theorem to find the coefficient of \( x^{5} y^{4} \) in the expansion of \( (x+y+2)^{10} \).