An urn contains 4 green , 5 blue ,2 red and 3yellow marbles .
If three marbles are drawn at random , what is the probability that none is green ?

Options

A. `(2)/(7)`
B. `(253)/(728)`
C. `(10)/(21)`
D. none of these

Answer

D

Explanation

According to question
`n(S)=""^(14)C_(3)=(14!)/((14-3)!3!)=(14xx13xx12)/(3xx2xx1)=364`
`and n( E)=""^(10)C_(3)=(10!)/((10-3)!3!)=(10xx9xx8)/(3xx2xx1)=120`
`implies ` Required probability `=(N( E))/(n(S))=(120)/(364)=(30)/(91)`