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. Then, y/x is equal to

The 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 words where no letter is repeated. Choosing the word where no letter is repeated can be done in 10! ways
∴ x = 10!
Let y be the number of words where exactly one letter is repeated twice.
Since one letter is repeated,
We can choose one repeatedly letter out of 10 letters and can be done in 10C1 ways, then place them on any two places, which can be done in 10C2 ways.
Now, choose 8 out of 9 remaining letters which can be done in 9C8 ways. And then, we can arrange that 8 non-repeated letters in 8! ways.
∴ y = 10C1 × 10C2 × 9C8 × 8! = 10 × 45 × 9 × 8!
Then y/x = (10 × 45 × 9 × 8!) / (10!) = (10 × 45 × 9 × 8!) / (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) = 5