If the letters of the word ATTRACTION are written down at random, find the probability that i.                all the T ‘s occur together

Explanation

Step 1: Find number of arrangements in which all T’s occur together.


T’s occur together `=(8!)/(2!)` [A chain of 3 T’s and 7 letters]

Total arrangements=`(10!)/(3!⋅2!)`​


Step 2: Find probability by taking ratio of favorable and total outcomes.


P (All T’s together) =`[(8!)/(2!)]/[(10!)/(3!⋅2!)]`