Permutation

john-1 · #1 $Old$ November 6th, 2009, 12:32 PM

Fran is working on a word puzzle and is looking for four-letter "scrambles" from the clue word calculate.

How many of the possible four-letter scrambles contain four different letters?

I don't get this question at all, can someone explain it to me as well as their solution. There isn't any solution for this question in my textbook at the back. Please help. Thank you very much!

Plato · #2 $Old$ November 6th, 2009, 12:49 PM

Quote:

Originally Posted by john-1 $View Post$

Fran is working on a word puzzle and is looking for four-letter "scrambles" from the clue word calculate.

How many of the possible four-letter scrambles contain four different letters?

There are six different letters: $C~A~L~U~T~E$ .
$_6\mathcal{P}_4=(6)(5)(4)(3)$ .

john-1 · #3 $Old$ November 6th, 2009, 01:03 PM

so the question is basically asking how many different combinations can you form out of the six letters, with four letters?

then the answer would be 360?

Plato · #4 $Old$ November 6th, 2009, 01:07 PM

Quote:

Originally Posted by john-1 $View Post$

so the question is basically asking how many different combinations can you form out of the six letters, with four letters? then the answer would be 360?

It is not combinations but permutations.
Note that it said different letters.
So we cannot use two a's for example.