Find the probability that in a random arrangement of the letters of the word "INSTITUTION" the three T's are together - Maths - Probability

Question

Find the probability that in a random arrangement of the letters of
the word "INSTITUTION" the three T's are together

Bagath · Answer

Given word: INSTITUTION
Total letters = 11
The word contains 3 I, 2 N, 1 S, 3 T, 1 U and 1 O
Total number of arrangement = 11!/(3!*2!*3!) = 554400
Now, taken 3 T are together
So total latter = 9
The number of favorable cases = 9!/(3!*2!) = 30240
Now, P(3 T are togather) = 30240/554400 = 0 0545

Find the probability that in a random arrangement of the letters of the word "INSTITUTION" the three T's are together.