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A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?

A. 22

B. 13

C. 24

D. 52

E. None of these

Answer: Option E

Solution(By Examveda Team)

Required number of ways
$$ = \left( {{}^4{C_4} \times {}^6{C_1}} \right) + $$   $$\left( {{}^3{C_3} \times {}^4{C_{2}}} \right)$$
$$\eqalign{ & = \left( {1 \times 6} \right) + \left( {1 \times \frac{{4 \times 3}}{2}} \right) \cr & = \left( {6 + 6} \right) \cr & = 12 \cr} $$

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Comments ( 2 )

  1. Neeraja Sanapala
    Neeraja Sanapala :
    3 years ago

    yes answer is not 14 it is 12

  2. Raja Sekhar
    Raja Sekhar :
    3 years ago

    How come fourteen... it’s should be twelve I think
    = (4C4X6C1) + (3C3X4C2)
    = (1X6) + (1X4*3/2)
    = 6+6 = 12

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