In a class , there are 15 boys and 10girls / three students are selected at random . The probability that I girl and 2 boys are selected , is ,

Options

A. `(21)/(46)`
B. `(25)/(117)`
C. `(1)/(50)`
D. `(3)/(25)`

Answer

A

Explanation

Let S be the sample space and E be the event of selecting 1girl and 2 boys .
then n(S) =Number ways of selecting 3 students out of 25
`=""^(25)C_(3)`
`=((25xx24xx23))/((3xx2xx1))=2300.`
also ,n(E) `=(""^(10)C_(1)xx""^(15)C_(2))`
` =[10xx(15xx14)/(2xx1)]`
`=1050.`
`therefore P(E) =(n(E))/(n(S))=(1050)/(2300)=(21)/(46)`