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
- A19
- B21
- C46
- 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