An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn, is

Options

A. `(40)/(143)`
B. `(70)/(143)`
C. `(3)/(13)`
D. `(10)/(13)`

Answer

D

Explanation

Total number of ways of selecting 3 balls `= .^(13)C_(3)` and number of ways of selecting 3 balls including both colours
`= .^(8)C_(2)xx .^(5)C_(1)+ .^(8)C_(1)xx .^(5)C_(2)`
Hence, the probability that balls of both colours are drawn
`=(.^(8)C_(2)xx .^(5)C_(1)+ .^(8)C_(1)xx .^(5)C_(2))/(.^(13)C_(3))=(140+80)/(286)`
`=(220)/(286)=(110)/(143)=(10)/(13)`