Words of length 10 are formed using the letters A, B, C, D, E, F,...

$x =$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} \times {}^{9}{C}_{8} \times \dfrac{10 !}{2 !}$$= 10 \times 9 \times \dfrac{10 !}{2 !} = 5 \times 9 \times 10 !$

$\dfrac{y}{9x} = \dfrac{5 \times 9 \times 10 !}{9 \times 10 !} = 5$