In an avionics mission computer, 4 critical navigation tasks and 3 sensor monitoring tasks are to be scheduled in sequence. In how many distinct ways can all 7 tasks be scheduled if all 4 navigation tasks must be executed consecutively as an unbroken block?

(A) 576

(B) 144

(C) 288

(D) 720

Answer Key:

A

### Solution: Treat the 4 navigation tasks as 1 block. Total items to arrange = $1 \text{ (block)} + 3 \text{ (sensor tasks)} = 4$ items $\implies 4! = 24$. Within the block, the 4 tasks can be arranged in $4! = 24$ ways. Total = $24 \times 24 = 576$. Correct: A.

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