We will say that a rearrangement of the letters of a word has no fixed letters if. When the rearrangement is placed directly below the word, no column has the same letter repeated. For instance, HBRATA is a rearrangement with no fixed letters of BHARAT. How many distinguishable rearrangement with no fixed letters does BHARAThave? (The two A's are considered identical)

Step-by-step solution

Let use assume the 2 A^ 's to A₁ and A₂ BHA ₁ RA ₂ ~T Number of rearrangements of these 6. = 6 ( 1 2 - 1 3 + 1 4 - 1 5 + 1 6 )=265 . Let P be the set when A₂ occupies place of A₁ and be the set when A₁ occupies place of A₂ array ll n(P)=53, & n(Q)=53 n(n Q)=9 & array Hence required arrangements aligned & = 1 2 (265-n(P Q)) & = 1 2 (265-106+9) & = 168 2 =84 aligned