Explanation

(c)
ASSISTANT : A A I N SSS TT
STATISTICS : A C II SSS TTT
Same letters can be A, I, S, T
Probability of choosing, $A = \frac{{\ ^{2}C}_{1}}{{\ ^{9}C}_{1}} \times \frac{{\ ^{1}C}_{1}}{{\ ^{10}C}_{1}} = \frac{1}{45}$
Probability choosing, $I = \frac{{\ ^{1}C}_{1}}{{\ ^{9}C}_{1}} \times \frac{{\ ^{2}C}_{1}}{{\ ^{10}C}_{1}} = \frac{1}{45}$
Probability of choosing, $S = \frac{{\ ^{3}C}_{1}}{{\ ^{9}C}_{1}} \times \frac{{\ ^{3}C}_{1}}{{\ ^{10}C}_{1}} = \frac{1}{10}$
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 $= \frac{19}{90}$