how many 4-letter codes can be formed using the letters A, B, C, D, E, and F? No letter can be used more than once.

Question

What is the answer to this question?

Answer 1

₆C₄ ways to choose the 4 letters.  4! ways to make a code of 4 letters. ₆C₄=15, 4!=24, and 15×24=360

Answer 2

The answer is 360. 

 

There is a total of 6 possible letters to choose from. 

 

Let's say all of the letters written down on pieces of paper and placed in a hat. 

You choose the letters one by one, and once the piece of paper has been chosen, you do not put it back in the hat. 

 

What are your chances of choosing an "A" on the first draw?

1/6

 

Let's pretend you draw a "C" on your first draw. What are your (different) chances of drawing an "A" this time?

1/5

 

Because you have taken a letter out of the hat, only 5 letters remain, meaning you have a higher chance of getting what you want (in this case an A). 

 

Repeat this twice more.

 

So the chances of drawing an A on an trial is as follows.

 

1/6, 1/5, 1/4, 1/3

 

Multiply all of these probabilities together (we are assuming these are independent drawings) and you get 1/360. Take the reciprocal of that number and you get the total possible combinations.. 360.