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:Options3/9619/136None19/90

To solve this problem, we need to calculate the probability of drawing the same letter from both words.

Step 1: Count the number of letters in each word. 'ASSISTANT' has 9 letters and 'STATISTICS' has 10 letters.

Step 2: Calculate the total number of possible outcomes. This is simply the product of the number of letters in each word, which is 9*10 = 90.

Step 3: Count the number of each letter in both words. In 'ASSISTANT', there are 3 S's, 2 A's, 1 I, 1 T, 1 N, and 1 T. In 'STATISTICS', there are 3 S's, 3 T's, 2 I's, 1 A, and 1 C.

Step 4: Calculate the number of favorable outcomes. This is the sum of the products of the counts of each letter in both words. For S, it's 33 = 9. For A, it's 21 = 2. For I, it's 12 = 2. For T, it's 13 = 3. For N, it's 10 = 0 (since there's no N in 'STATISTICS'). For T, it's 13 = 3. Adding these up, we get 9+2+2+3+0+3 = 19.

Step 5: Calculate the probability. The probability is the number of favorable outcomes divided by the total number of possible outcomes, which is 19/90.

So, the correct answer is 19/90.