Question

A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is

• A. $\frac { 5 } { 11 }$
• B. $\frac { 21 } { 55 }$
• C. $\frac { 4 } { 11 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 21 } { 55 }$

Answer 2

Required probability $= \frac { { } ^ { 7 } C _ { 2 } } { { } ^ { 11 } C _ { 2 } } = \frac { 7 \cdot 6 } { 11 \cdot 10 } = \frac { 21 } { 55 }$.