Sequential Elimination Race

Three players with independent lifetimes $X_1 \sim \operatorname{Exp}(1)$, $X_2 \sim \operatorname{Exp}(2)$, $X_3 \sim \operatorname{Exp}(4)$ compete. The first to "die" is eliminated, then the two survivors continue (by memorylessness, their residual lifetimes are fresh exponentials with the same rates). The second to die is eliminated, and the last survivor wins.

(a) Find the probability that the elimination order is $X_3, X_1, X_2$ (i.e., player 3 dies first, then player 1, then player 2).

(b) Find the expected total time until only one player remains.