The total number of words (with or without meaning) that can be...

Given,

Word $' DISTRIBUTION '$

Now, we have $III, TT, D, S, R, B, U, O, N$

Number of words with $3$ alike letter and $1$ different will be,

${=}^{8}{C}_{1} \times \dfrac{4 !}{3 !} = 32$

Number of words with $2$ alike and other $2$ alike will be,

$= \dfrac{4 !}{2 ! 2 !} = 6$

Number of words with $2$ alike and $2$ different will be,

${=}^{2}{C}_{1}{\times}^{8}{C}_{2} \times \dfrac{4 !}{2 !} = 672$

Number of words with all different letters will be,

${=}^{9}{C}_{4} \times 4 ! = 3024$

Therefore, the total number of ways will be,

$= 3024 + 672 + 6 + 32$

$= 3734$