An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

Options

A. `1//2`
B. `2//23`
C. `1//3`
D. `2//7`

Answer

D

Explanation

Total number of elementary events `=.^(9)C_(3)`
Favourable number of elementary events `= .^(3)C_(1)xx .^(4)C_(1)xx .^(2)C_(1)`
`therefore` Required probability `=(.^(3)C_(1)xx .^(4)C_(1)xx .^(2)C_(1))/(.^(9)C_(3))=(2)/(7)`