Set Letters
How many 3 letter code symbols can be formed using a set of 5 diff. letters if repetition is not allowed?
5P3 = 5! / (5-3)! = 60
A day later:
Sometimes it occurs to me that a better explanation may help.
The total number of 3-letter groups possible using a 5-letter alphabet is
5^3 = 125
Excluding those that repeat a letter makes this a question of permutations. We have 5 choices for the first letter, but after that choice (whatever we choose) there are only 4 choices for the second letter, and that leaves only 3 choices for the third. That’s
5 * 4 * 3 = 60
and we can use the general formula for permutations,
5P3 = 5! / (5-3)! = 5! / 2!
= 5 * 4 * 3 * 2 * 1 / (2 * 1)
This formula is constructed by noting that if we chose 5-letter code groups, without repetition, we would have 5! permutations by the same reasoning as above, but since we are not choosing the last two letters, we can divide that by the 2! choices we would have had for those letters in any particular case.
The third common calculation is combinations, in which we disregard differences of order: ABC and BAC and CBA are all the same combination. The formula for combinations divides the number of permutations by the number of different orders in which any given combination can appear:
5C3 = 5! / [(5-3)! 3!] = 10
For this problem, we calculate permutations, because it makes a difference in what order the letters appear (that is, how we “permute” them).
I’m adding this more extensive explanation because the question asked was so basic that I suspect a bit of tutorial material might help you. If it repeats material you know, I apologize. But if you are tackling problems like this, you should learn to recognize and apply each of these calculations easily.
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