How many 3 letter combinations can be made from 10 letters?

Answer 1

The number of 3 letter different combinations that can be made from 10 different

letters is given by: 10C3 = 10!/[3!(10-3)!] = 120different 3 letter combinations.

The number of three letter different permutations (one given 3 letter combination

gives 3! = 6 different permutations, e.g., the combination abc gives the 9

permutations, abc, acb, bac, cab, bca, cba) is given by 10P3 = 10!/(10-3)! = 720

different 3 letter permutations.

The symbol (!) is the operator called "factorial" and it implies the multiplication:

n! = n∙(n-1)! = n∙(n-1)∙(n-2)! = n(n-1)(n-2)(n-3)...(4)(3)(2)(1)(0!)

where 0! = 1.

i.g., 6! = 6∙5∙4∙3∙2∙1 = 720