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

Options

A. `(1)/(45)`
B. `(13)/(90)`
C. `(19)/(90)`
D. None of these

Answer

C

Explanation

Given, ASSISTANT `to` AA I N SSS TT
STATISTICS `to` AC II SSS TTT
Same letters can A, I, S, T.
Probability of choosing `'A' = (.^(2)C_(1))/(.^(9)C_(1))xx(.^(1)C_(1))/(.^(10)C_(1))=(2)/(9)xx(1)/(10)=(1)/(45)`
Probability of choosing `'I'=(1)/(.^(9)C_(1))xx(.^(2)C_(1))/(.^(10)C_(1))=(1)/(9)xx(2)/(10)=(1)/(45)`
Probability of choosing `'S' = (.^(3)C_(1))/(.^(9)C_(1))xx(.^(3)C_(1))/(.^(10)C_(1))xx(3)/(9)xx(3)/(10)=(1)/(10)`
Probability of choosing `'T' = (.^(2)C_(1))/(.^(9)C_(1))xx(.^(3)C_(1))/(.^(10)C_(1))=(2)/(9)xx(3)/(10)=(1)/(15)`
Hence, the required probability `=(1)/(45)+(1)/(45)+(1)/(10)+(1)/(15)=(19)/(90)`