1.

An urn contains 4 green, 5 blue ,2 red and3yellow marbles .If eightmarblesare drawnat random , whatis theprobabilitythat thereare equalnumberof marblesofeachcolour ?

Answer»

`(4)/(7)`
`(361)/(728)`
`(60)/(1001)`
`(1)/(1)`

SOLUTION :Accordingto 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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