Question

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

• A. $\frac{3}{9}$
• B. $\frac{8}{9}$
• C. $\frac{5}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is C $\frac{5}{9}$

There are nine letters in the word 'EQUATIONS' out of which five are vowels and four are consonants.
Two letters can be chosen in ${}^9{C}_2$ ways.
One vowel and one consonant can be chosen in ${}^5{C}_1\times {}^4{C}_1$ ways.
$\therefore$ Required probability $=\frac{{}^5{C}_1\times {}^4{C}_1}{{}^9{C}_2}=\frac{5}{9}$
OR,
Probability that one letter is vowel and other is consonant $=P\left(V\right).P\left(C\right)+P\left(C\right).P\left(V\right)=\frac{5}{9}\times \frac{4}{8}+\frac{4}{9}\times \frac{5}{8}=\frac{5}{9}$