That is correct!
Had it been without repeating, you would have had: 26.25.24.23.10.9.8
This seems like a pretty straightforward question but I feel like I'm missing something.
Suppose I wanted to construct a pin number that contains 4 letters of the alphabet and 3 numbers (0 to 9) in no particular order, and I can use the same letter/number more than once.
My pin will be 7 letters/numbers in length.
I have:
(26)(26)(26)(26)(10)(10)(10)
= 456 976 000
It feels like I'm missing something or is the question really this straightforward?
Any help is appreciated!
Your calculation counted the amount of pin numbers in the sequence LLLLDDD, where L is a letter and D is a digit,
allowing repetition.
That's fine if no shuffling of the letters among the digits is allowed.
(If you meant that the 4 letters are in direct sequence "in no particular order" and same for the digits).
We choose 4 of the 7 positions for the 4 letters.
That automatically leaves us with 3 positions for the 3 digits.
Now you have alternatives for the letters and alternatives for the digits in that particular sequence.
the sequence could be LDLDLDL
Now choose a new sequence and you have the same alternatives for the letters and for the digits.
The number of such "letter-digit" sequences is
as you need to choose 4 of the 7 positions for letters
or instead choose 3 of the 7 positions for the digits (same thing).
Hence you need to count the number of ways this can be done.