Explanation
We are given the following words:
• FARMHOUSE
,
• GUILDHALLS
We are required to determine the number of ways to arrange the letters in the words above.
For Question A:
This can be achieved as follows:
[tex]\begin{gathered} Total\text{ }letters=9 \\ Also,\text{ }there\text{ }are\text{ }no\text{ }duplicate\text{ }letters \\ \therefore9!=9\times8\times7\times6\times5\times4\times3\times2\times1 \\ =326,880\text{ }ways\text{ } \end{gathered}[/tex]
For Question B:
This can be achieved as follows:
[tex]\begin{gathered} Total\text{ }letters=10 \\ Duplicate\text{ }letter:L=3 \\ \therefore\frac{10!}{3!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1} \\ =10\times9\times8\times7\times6\times5\times4 \\ =604,800\text{ }ways \end{gathered}[/tex]
Hence, the answers are:
(a) 326,880 ways
(b) 604,800 ways
