Question

The word "theory" is composed of the letters of the split alphabet. Three cards are taken out at random and stacked in a row one after another in order of appearance. How many possible compounds can be made up of the letters of this word?

Answer 1

There would be
`120` of them.

Explanation:

There are
`6` distinct letters in the word "
`\verb!theory!`".

Hence, there would
`6` possible choices for the first letter that was selected.

Since the chosen card won't be placed back in the pool, there would be only
`(6 - 1) = 5` possible choices for the second letter.

Likewise, there would be
`(6 - 2) = 4` choices for the third letter.

`6 * 5 * 4 = 120`. In other words, there are
`120` possible ways to draw three cards out of
`6` one after another.

Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "
`\verb!the!`" and "
`\verb!het!`" from the number of combinations.