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. $\frac{35}{96}$
• B. $\frac{19}{90}$
• C. $\frac{19}{96}$
• D. $noneofthese$

Answer 1

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

ASSISTANT $\to$ AA I N SSS TT
STATISTICS $\to$ A II C SSS TTT
Here N and C are not common and same letters can be A, T. Therefore
Probability of choosing A = $\frac{{}^2{C}_1}{{}^9{C}_1}\times \frac{{}^1{C}_1}{{}^{10}{C}_1}=\frac{1}{45}$
Probability of choosing I = $\frac{1}{{}^9{C}_1}\times \frac{{}^2{C}_1}{{}^{10}{C}_1}=\frac{1}{45}$
Probability of choosing S = $\frac{{}^3{C}_1}{{}^9{C}_1}\times \frac{{}^3{C}_1}{{}^{10}{C}_1}=\frac{1}{10}$
Probability of choosing T = $\frac{{}^2{C}_1}{{}^9{C}_1}\times \frac{{}^3{C}_1}{{}^{10}{C}_1}=\frac{1}{15}$
Hence, required probability
$=\frac{1}{45}+\frac{1}{45}+\frac{1}{10}+\frac{1}{15}=\frac{19}{90}$