A) \[19/45\]
B) \[19/90\]
C) \[89/90\]
D) \[1/90\]
Correct Answer: B
Solution :
The letters of the word'ASSISTANT5 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 \[=\frac{2}{90}+\frac{2}{90}+\frac{9}{90}+\frac{6}{90}=\frac{19}{90}\]
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