The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike.is ...... .

The given word ie 'SYLLABUS' having letters SS, LL,
ABUY.
Now, number of ways to select two like letters are ${ }^2{\mathrm{C}}_1$.
And number of ways to select two distinct letters are${ }^5{C}_2$
And number of ways to permutate the 2 like letters and 2 distinct letters is $\frac{4!}{2!}$
So, number of required words

$\begin{array}{c}{=}^2{\mathrm{C}}_1{\times }^5{\mathrm{C}}_2\times \frac{4!}{2!}\\ =2\times 10\times 12\\ =240\end{array}$