An urn contains `9` balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

Options

A. a) `5/(84)`
B. b) `3/9`
C. c) `3/7`
D. d) `7/(17)`

Answer

a) `5/(84)`

Explanation

`3` balls drawn from `9` balls in `9_(C_3)=84` ways.


There are two red balls.


Three balls of the same color can be drawn in two ways:


`3` out of `3` blue balls or `3` ot of `4` black balls


Probability `= (3_(C_3))/84+(4_(C_3))/84`


Required probability `=1/84+4/84`


`=5/84`


Hence, correct options is a)