Probability · Question 9

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The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

129182
1726
1926
103182

Answer

(1) 129182

Solution

Total persons = 16 ⇒ n(S) = 16C12 = 16C4 = 1820

Favourable cases (engineers E, doctors D, professors P):

E = 3, D = 1, P = 8: 4C3 2C1 10C8 = 4 2 45 = 360

E = 3, D = 2, P = 7: 4C3 2C2 10C7 = 4 1 120 = 480

E = 4, D = 1, P = 7: 4C4 2C1 10C7 = 1 2 120 = 240

E = 4, D = 2, P = 6: 4C4 2C2 10C6 = 1 1 210 = 210

⇒ n(E) = 360 + 480 + 240 + 210 = 1290

∴ P = 12901820 = 129182

Answer: (1)

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