An attitude and heading reference system (AHRS) utilizes 7 rate gyroscopes, of which exactly 3 are triple-modular redundant (TMR) units. If an engineer randomly selects 3 gyroscopes for vibration qualification testing, what is the probability that exactly 2 of the selected gyroscopes are TMR units?

(A) 12/35

(B) 18/35

(C) 6/35

(D) 9/35

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Sample Space:** Total combinations $\binom{7}{3} = 35$. 2. **Stage 2: Favorable Combinations:** We require 2 from the 3 TMR units ($\binom{3}{2} = 3$) and 1 from the remaining 4 units ($\binom{4}{1} = 4$). 3. **Stage 3: Favorable Total:** $3 \times 4 = 12$. 4. **Stage 4: Probability:** $P = 12/35$. 5. **Stage 5: Selection:** Option A is correct.

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