A flight test safety review board of 4 members is to be formed from a panel of 5 aerodynamics experts and 4 propulsion experts. If the committee must contain at least 2 aerodynamics experts and at least 1 propulsion expert, in how many distinct ways can the board be selected?

Answer Key:

100

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Problem Constraints:** Total committee size = 4 members from 5 Aero and 4 Prop experts. Conditions: Aero $\ge 2$, Prop $\ge 1$. 2. **Stage 2: Permissible Cases:** * Case 1: 2 Aerodynamics experts AND 2 Propulsion experts. * Case 2: 3 Aerodynamics experts AND 1 Propulsion expert. * (4 Aero and 0 Prop violates Prop $\ge 1$; 1 Aero and 3 Prop violates Aero $\ge 2$). 3. **Stage 3: Combinatorial Computation:** * Case 1: $\binom{5}{2} \times \binom{4}{2} = \frac{5 \times 4}{2} \times \frac{4 \times 3}{2} = 10 \times 6 = 60$. * Case 2: $\binom{5}{3} \times \binom{4}{1} = 10 \times 4 = 40$. 4. **Stage 4: Total Selection Ways:** Total $= 60 + 40 = 100$. 5. **Stage 5: Official Reference:** R.S. Aggarwal, *Quantitative Aptitude*, Chapter 30 (Permutations & Combinations).

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