Question

A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letters is

• A. $\frac{1}{45}$
• B. $\frac{12}{90}$
• C. $\frac{19}{90}$
• D. None of these

Answer 1

The correct option is C $\frac{19}{90}$

In 'ASSISTANT' and 'STATISTICS', the same letters are A,I,S,T

Probability of choosing $A=\frac{{{}^{2}C}_1}{{{}^{9}C}_1}\times \frac{{{}^{1}C}_1}{{{}^{10}C}_1}=\frac{1}{45}$

$I=\frac{{{}^{1}C}_1}{{{}^{9}C}_1}\times \frac{{{}^{2}C}_1}{{{}^{10}C}_1}=\frac{1}{45}$

$S=\frac{{{}^{3}C}_1}{{{}^{9}C}_1}\times \frac{{{}^{3}C}_1}{{{}^{10}C}_1}=\frac{1}{10}$

$T=\frac{{{}^{2}C}_1}{{{}^{9}C}_1}\times \frac{{{}^{3}C}_1}{{{}^{10}C}_1}=\frac{1}{15}$

So, total probability
$=\frac{1}{45}+\frac{1}{45}+\frac{1}{10}+\frac{1}{15}=\frac{19}{90}$