Question

Find the number of ways to arrange the letters in the following words.a. FARMHOUSEb. GUILDHALLS

Answer 1

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:

`\begin{gathered} Total\text{ }letters=9 \\ Also,\text{ }there\text{ }are\text{ }no\text{ }duplicate\text{ }letters \\ \therefore9!=9*8*7*6*5*4*3*2*1 \\ =326,880\text{ }ways\text{ } \end{gathered}`

For Question B:

This can be achieved as follows:

`\begin{gathered} Total\text{ }letters=10 \\ Duplicate\text{ }letter:L=3 \\ \therefore(10!)/(3!)=(10*9*8*7*6*5*4*3*2*1)/(3*2*1) \\ =10*9*8*7*6*5*4 \\ =604,800\text{ }ways \end{gathered}`

Hence, the answers are:

(a) 326,880 ways

(b) 604,800 ways