Question

3. How many four letter codes can be made from the English alphabet? Uppercase and Lowercase letters can

be used (this means A is different from a) and the letters can be repeated.


4. How will your answer change from problem 3 if the letters cannot be repeated?

Answer 1

3) 7311616

4) 6497400

Explanation:

3) There are 26 letters in the alphabet

Total letters = total uppercase letters + total lowercase letters

= 26 + 26

= 52

Since the letters are allowed to be repeated, the number of ways:

52*52*52*52

= 52⁴

= 7311616

4) if the letters cannot be repeated then the number of ways is:

`^(52)P_4\\\\= (52!)/((52-4)!) \\\\= (52!)/(48!)\\ \\= (52*51*50*49*48!)/(48!) \\\\= 52*51*50*49\\\\=6497400`