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

ASSISTANT : AA I N SSS TT
STATISTICS : A C II SSS TTT
Same letters can be A, I, S, T
the Probability of choosing,$\mathrm{A}=\frac{{ }^2{\mathrm{C}}_1}{{ }^9{\mathrm{C}}_1}\times \frac{{ }^1{\mathrm{C}}_1}{{ }^{10}{\mathrm{C}}_1}=\frac{1}{45}$
the Probability of choosing $\mathrm{I}=\frac{{ }^1{\mathrm{C}}_1}{{ }^9{\mathrm{C}}_1}\times \frac{{ }^2{\mathrm{C}}_1}{{ }^{10}{\mathrm{C}}_1}=\frac{1}{45}$
the Probability of choosing $\mathrm{S}=\frac{{ }^3{\mathrm{C}}_1}{{ }^9{\mathrm{C}}_1}\times \frac{{ }^3{\mathrm{C}}_1}{{ }^{10}{\mathrm{C}}_1}=\frac{1}{10}$
the Probability of choosing $\mathrm{T}=\frac{{ }^2{\mathrm{C}}_1}{{ }^9{\mathrm{C}}_1}\times \frac{{ }^3{\mathrm{C}}_1}{{ }^{10}{\mathrm{C}}_1}=\frac{1}{15}$
So, total probability $=\frac{19}{90}$