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