A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

Question: A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

Solution:
For S = (3/9) × (3/10) = 1/10
For A = (2/9) × (1/10) = 1/45
For I = (1/9) × (2/10) = 1/45
For T = (2/9) × (3/10) = 1/15

Total probability = (1/10) + (1/45) + (1/45) + (1/15)
= 19/90