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15 votes
15 votes
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?

User Sschunara
by
2.8k points

1 Answer

17 votes
17 votes

Answer:

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.

User Shiraz
by
3.0k points
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