Question

In how many ways can three letter arrangments be made from the letters in the word: Computer?

Answer 1

Task. In how many ways can three letter arrangments be made from the letters in the word: “computer”?

Solution. Notice that the word “computer” consists of 8 letters and all of them are distinct.

Let $ABC$ be a three letter word where $A$, $B$ and $C$ are distinct letters from the word “computer”. Then the first letter $A$ can be choosen in 8 ways. For any choice of first letter there exists 7 choices of second letter $B$, and to any choice of $A$ and $B$ there exists 6 choices of third letter $C$.

Hence the number of three letter words is equal to

$8*7*6=336.$

Answer. 336.