Full Ordering Probability for Four Competing Exponentials

Four independent exponential random variables $X_1 \sim \operatorname{Exp}(1)$, $X_2 \sim \operatorname{Exp}(2)$, $X_3 \sim \operatorname{Exp}(3)$, $X_4 \sim \operatorname{Exp}(6)$ represent task completion times. Using iterated applications of the memoryless property, find $P(X_4 < X_3 < X_2 < X_1)$ — the probability that the tasks complete in the specific order 4, 3, 2, 1.