Question

Using

twotwo

of the letters of the​ alphabet, how many

fourfour​-letter

codes can we form if we are allowed to use the same letter more than​ once?

Answer 1

We first need to select two letter out of 26 available which can be done in ²⁶C₂ i.e. 325 ways.

Now, for every letter in the code, we have 2 choices. Hence,

Total number of codes = 2⁴ = 16

But in this, there would be 2 codes where all the four letter will be same but we need atleast two letters in code. Hence,

Number of possible codes for any 2 letter = 16 - 2 = 14

Therefore,

Total number of possible codes = 325*14 = 4550