Question

Determine the number of three letter arrangements using the letters of the word METAPHORa. 336b. 40 320 512c. 512d. 56

Answer 1

Given:

The word, "METAPHOR".

To find:

The number of three letter arrangements.

Explanation:

There are 8 letters.

Therefore, n = 8.

Out of 8 letters, we need to select 3 letters.

So, r = 3.

Using the permutation,

$\begin{gathered} ^8P_3=\frac{8!}{(8-3)!} \\ =\frac{8!}{5!} \\ =\frac{5!\times6\times7\times8}{5!} \\ =336 \end{gathered}$

Therefore, the number of three-letter arrangements is 336.

Final answer:

The number of three-letter arrangements is 336.