Question

A committee consists of 9 experts taken from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is

• A. $\frac { 1 } { 729 }$
• B. $\frac { 1 } { 24 }$
• C. $\frac { 1 } { 21 }$
• D. $\frac { 2 } { 7 }$

Answer 1

Answer: (D)

$\frac { 2 } { 7 }$

Answer 2

Required probability

$= \frac { { } ^ { 2 } C _ { 1 } \times { } ^ { 3 } C _ { 1 } \times { } ^ { 4 } C _ { 1 } } { { } ^ { 9 } C _ { 3 } } = \frac { 2 \times 3 \times 4 } { \left( \frac { 9 \times 8 \times 7 } { 3 \times 2 } \right) } = \frac { 2 } { 7 }$ .