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.

Step-by-step 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=(8!)/((8-3)!) \\ =(8!)/(5!) \\ =(5!*6*7*8)/(5!) \\ =336 \end{gathered}`

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

Final answer:

The number of three-letter arrangements is 336.