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KVPY2015MathematicsProbability

An urn contains marbles of four colours: red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely: (1) the selection of four red marbles; (2) the selection of one white and three red marbles; (3) the selection of one white, one blue and two red marbles; (4) the selection of one marble of each colour. The smallest total number of marbles satisfying the given

Options

  1. A19
  2. B21
  3. C46
  4. D69

Correct answer

B. 21

Step-by-step solution

Let number of red, white, blue, green balls be r, w, b, g respectively and r+w+b+ g = n r ( r -1)( r -2)( r -3) 24 = wr ( r -1)( r -2) 6 = wbr ( r -1) 2 = r w b . g r -3=4 w , r -2=3 ~b , r -1=2 ~g r =4 w +3, r =3 ~b +2, r =2 ~g +1 Now LCM of (4,3,2)=12 array l r_ =11 w_ =2 b_ =3 g_ =5 (r+w+b+g)_ =21 array

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