Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, y 9 x =

Step-by-step solution

x = number of ways in which 10 letter word can be formed using the given ten distinct letters. x = 10 ! y = number of ways, in which 10 letter words can be formed, in which exactly 1 letter is repeated twice and remaining 8 letters are distinct. y =   10 C 1 ×   9 C 8 × 10 ! 2 ! = 10 × 9 × 10 ! 2 ! = 5 × 9 × 10 ! y 9 x = 5 × 9 × 10 ! 9 × 10 ! = 5