**Q. 2-Part Questions!**

(a) How many different three-letter initials can people have?

(b) How many different three-letter initials with none of the letters repeated can

people have?

A:

(a) OK. We have three-letter initials, that means we have three slots to fill: __ __ __.

How many choices for the first slot? 26, right? There are 26 letters. 26 __ __.

How many choices for the second slot? 26 again for the 26 different letters: 26 26 __.

And finally, also 26 options for the last slot: 26 26 26.

So, the answer is that there are 26*26*26 = 26³ different three-letter initials.

(b) Now, the same concept, but *no* repetitions. Start with 3 blank slots: __ __ __.

How many choices for the 1st slot? 26 different letters means 26 choices: 26 __ __

How many choices for the 2nd slot? Remember, we cannot repeat. Therefore, there are only 25 choices now: 26 25 __

How many choices for the 3rd and final slot? No repeating means only 24 options now: 26 25 24.

So, there are 26*25*24 different ways.

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wow, you make it look very easy for me, i am grasping it more now, thanks 🙂