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

The correct option is B

$\frac{21}{55}$

Explanation for the correct option:

Step 1: Find the total favourable cases:

As there are $7$ constants and $2$ have to be chosen.

So, the Favourable number of ways $={}^{7}C_2$

Step 2: Find the total number of cases:

As there are $11$ constants and $2$ have to be chosen.

So, the total number of cases $={}^{11}C_2$

Step 3: Find the probability of selecting $2$ constants:

Find the probability by dividing favourable cases by the total number of cases.

$\begin{array}{rcl}p& =& \frac{{}^{7}C_2}{{}^{11}C_2}\\ & =& \frac{7\times 6}{11\times 10}\\ & =& \frac{21}{55}\end{array}$

Hence, option (B) is the correct .