How many different arrangements of 5 letters can be made from the 26 letters of the alphabet?

P (26, 5)

C (26, 5)

26!

Answer: P (26,5).

That is all the possible combinations of 5 letters made out from 26 letters.

That is 26! / [ 5! (26 - 5) ! ] = 26! / [5! 21! ] = 26*25*24*23*22*21! / [ 5! 21!] =

= 26*25*24*23*22 / [5*4*3*2*1] = 65,780 arrangements.