Answer to Question #72302 in Combinatorics | Number Theory for Sayem

Question

The number of letters in the language of a weird country is 5 and no one in that
country uses more than 3 letters to make a word. What is the highest number of
words one can make in that language?

Answer 1

If every letter can be used only once in any word, then we should use the formula A(m,n) = n!/(n - m)!
In this case n = 5, m = 3.
A(3,5) = 5!/(5 - 3)! = 1*2*3*4*5/(1*2) = 60 words.
If letters can be used 2 or 3 times in one word, then the number of possible words is:
A(m,k) = m^k.
In this case m = 5, k = 3.
A(m,k) = 5^3 = 125 words.