Question #72302
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?
country uses more than 3 letters to make a word. What is the highest number of
words one can make in that language?
Expert's answer
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.
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.
