Question

A letter is taken out at random from the word 'ASSISTANT and another is taken-out from the word 'STATISTICS'. The chance that the two selected letters are identical, is

• A. $19/45$
• B. $19/90$
• C. $89/90$
• D. $1/90$

Answer 1

Answer: (B)

The letters of the word 'ASSISTANT' are A, A, I, N, S, S, S, T, T and the letters of the word 'STATISTICS' are A, C, I, I, S, S, S, T, T, T
Case (i) W letter is taken from each of the word, then its probability $P(A)=\frac{{}^2{C}_1}{{}^9{C}_1}\times \frac{{}^1{C}_1}{{}^{10}{C}_1}=\frac{2}{90}$
Case (ii) 'I' letter is taken from each of the word, then its probability $P(I)=\frac{{}^1{C}_1}{{}^9{C}_1}\times \frac{{}^2{C}_1}{{}^{10}{C}_1}=\frac{2}{90}$
Case (iii) 'S' letter is taken from each of the word, then its probability
$P(S)=\frac{{}^3{C}_1}{{}^9{C}_1}\times \frac{{}^3{C}_1}{{}^{10}{C}_1}=\frac{9}{90}$
Case (iv) 'T' letter is taken from each of the word, then its probability
$P(T)=\frac{{}^2{C}_1}{{}^9{C}_1}\times \frac{{}^3{C}_1}{{}^{10}{C}_1}=\frac{6}{90}$
Combined probability
$=\frac{2}{90}+\frac{2}{90}+\frac{9}{90}+\frac{6}{90}=\frac{19}{90}$