How many 3-letter combinations are possible from the first seven letters of the alphabet?
Permutations of 7 items taken 3 at a time.
The order matters so it is permutations, not combinations.
Look at "ordered subsets" in the link:
http://dwb4.unl.edu/Chem/CHEM869N/CHEM869NMats/Permutations.html
7! / (7-3)! = 7!/4! = 7*6*5 = 210
To find the number of 3-letter combinations possible from the first seven letters of the alphabet, we can use the concept of permutations.
Since we are selecting 3 out of 7 letters, we need to calculate the number of permutations of 3 letters taken from a set of 7 letters. The formula for the number of permutations is:
P(n,r) = n! / (n - r)!
Where P(n,r) represents the number of permutations of r objects taken from a set of n objects.
In this case, n = 7 (the number of letters in the set) and r = 3 (the number of letters we want to select).
Using the formula, we can calculate:
P(7,3) = 7! / (7 - 3)!
= 7! / 4!
= (7 * 6 * 5 * 4!) / 4!
= (7 * 6 * 5)
= 210
Therefore, there are 210 possible 3-letter combinations from the first seven letters of the alphabet.