If the letters of the word "ASSASSINATION" are arranged at random in a row, then the probability that no two A^ 's come together is equal to

Step-by-step solution

The number of all possible ways to arrange the letters of word ASSASSINATION is = 13 ! 3 ! 4 ! 2 ! 2 ! Now, the number of ways to arrange the letters S, S, S, S, I, N, T, I, O, N is 10 ! 4 ! 2 ! 2 ! and the three A^ s we must arrange between the gaps or at the end positions and it can be done in ¹¹ C₃ . So, required probability = 10 ! 4 ! 2 ! 2 ! ¹¹ C₃ 13 ! 3 ! 4 ! 2 ! 2 ! = 3 ! 11 10 9 3 ! 13 12 11 = 10 9 13 12 = 5 3 13 2 = 15 26