The letters of the word 'QUESTION' are arranged in a row at random. The probability that there are exactly two letters between Q and S is

Step-by-step solution

The given word is 'QUESTION', let E be the event that there are exactly two letters between Q and S . Here, number of sample space, n(S)=8 ! number of possible events, n(E)= ^6 P₂ 2 ! 5 ! Required probability aligned & P(E)= n(E) n(S) = ^6 P₂ 2 ! 5 ! 8 ! = 6 ! 2 ! 5 ! 4 ! 8 ! & = 6 ! 2 ! 5 ! 4 ! 4 ! 7 8 6 ! = 2 5 7 8 = 5 28 aligned