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

Solution:

Five letters can be chosen from the 26 alphabet letters in the following combinations.

\(^{26}{C_5}\) = 26!/(21! 5!) = (26 × 25 × 24 × 23 × 22 × 21!)/(21! 5!)

= (26 × 25 × 24 × 23 × 22)/120

= (26 × 5 × 23 × 22) = 65,780 ways

The five letters selected in each group can be arranged in 5! Ways or 120 ways. Therefore the different arrangements of five letters that can be made from 26 letters of the alphabet are

65,780 × 5! ways = 65,780 × 120 = 7,893,600 ways

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

Summary:

The different arrangements of five letters that can be made from 26 letters of the alphabet are 7,893,600 ways.