A hotel gives every customer who makes a reservation a confirmation code. How many different confirmation codes can be created if each code has 4 letters followed by 2 numbers?
letters a through z. There are 26 on my keyboard
order matters so permutations of 26 taken 4 at a time
= 26!/[22!]= 26*25*24*23
10 numbers (0 through 9)
again order matters
= 10!/8! = 10*9
so in the end
10*9*26*25*24*23
To determine the number of different confirmation codes that can be created, we need to consider the number of possibilities for each character position in the code.
For the first letter position, there are 26 possible choices (A-Z), since we have 26 letters in the English alphabet. Similarly, for the second, third, and fourth letter positions, there are also 26 possible choices each.
For the first number position, there are 10 possible choices (0-9), since we have 10 numbers. The same applies to the second number position as well.
Since the number of possibilities is independent for each character position, we can multiply the number of choices together to find the total number of confirmation codes.
Total number of confirmation codes = Number of choices for letter position 1 * Number of choices for letter position 2 * Number of choices for letter position 3 * Number of choices for letter position 4 * Number of choices for number position 1 * Number of choices for number position 2
Total number of confirmation codes = 26 * 26 * 26 * 26 * 10 * 10
Simplifying the expression:
Total number of confirmation codes = 26^4 * 10^2
Calculating this:
Total number of confirmation codes = 456,976,000
Therefore, there are 456,976,000 different confirmation codes that can be created.