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Question: An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at ra...

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 same colour is

A

584\frac { 5 } { 84 }

B

39\frac { 3 } { 9 }

C

37\frac { 3 } { 7 }

D

717\frac { 7 } { 17 }

Answer

584\frac { 5 } { 84 }

Explanation

Solution

P =3C3+4C39C3\frac { { } ^ { 3 } \mathrm { C } _ { 3 } + { } ^ { 4 } \mathrm { C } _ { 3 } } { { } ^ { 9 } \mathrm { C } _ { 3 } } = 1+484\frac { 1 + 4 } { 84 } = 584\frac { 5 } { 84 }