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
1/45
B
13/90
C
19/90
D
None of these

Solution:

ASSISTANT : AA I N SSS TT
STATISTICS : A C II SSS TTT
Same letters can be A, I, S, T
the Probability of choosing, $A = \frac{^{2} C_{1}}{^{9} C_{1}} \times \frac{^{1} C_{1}}{^{10} C_{1}} = \frac{1}{45}$
the Probability of choosing $I = \frac{^{1} C_{1}}{^{9} C_{1}} \times \frac{^{2} C_{1}}{^{10} C_{1}} = \frac{1}{45}$
the Probability of choosing $S = \frac{^{3} C_{1}}{^{9} C_{1}} \times \frac{^{3} C_{1}}{^{10} C_{1}} = \frac{1}{10}$
the Probability of choosing $T = \frac{^{2} C_{1}}{^{9} C_{1}} \times \frac{^{3} C_{1}}{^{10} C_{1}} = \frac{1}{15}$
So, total probability $= \frac{19}{90}$

Solution:

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