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An urn contains 4 green , 5 blue ,2 red and 3yellow marbles .
If eight marbles are drawn at random , what is the probability that there are equal number of marbles of each colour ?
A. `(4)/(7)`
B. `(361)/(728)`
C. `(60)/(1001)`
D. `(1)/(1)`

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Best answer
Correct Answer - C
According to question ,
`n(S) =""^(14)C_(8)=(14!)/((14-8)!8!)xx(14!)/(6!8!)`
`=(14xx13xx12xx11xx10xx9)/(6xx5xx4xx3xx2xx1)=3003`
`and n( E )=""^(4)C_(2)xx""^(5)C_(2)xx""^(2)C_(2)xx""^(3)C_(2)`
`=(4!)/((4-2)!2!)xx(5!)/((5-2)!2!)xx(2!)/((2-2)!2!)xx(3!)/((3-2)!2!)`
`=(4!)/(2!2!)xx(5!)/(3!2!)xx(2!)/(0!2)xx(3!)/(1!2!)`
`=(4xx3)/(2xx1)xx(5x4)/(2xx1)xx(1)/(1)xx(3)/(1)=180`
`implies ` Required probability `=(n(E))/(n(S))=(180)/(3003)=(60)/(1001)`

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