The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the…

From the given word, $\mathrm{S}-2,\mathrm{L}-2,\mathrm{A},\mathrm{B},\mathrm{Y},\mathrm{U}$.

Number of alike letter pairs $=2$

Number of ways to select one pair$={}^{2}C_1$

Number of distinct letters$=5$

Number of ways to select two distinct letters$={}^{5}C_2$

Number of ways to arrange four letters if two are alike$=\frac{4!}{2!}$

Required number of ways $={}^2\mathrm{C}_1{}^5\mathrm{C}_2·\frac{4!}{2!}=2·10·\frac{24}{2}=240$