how many 6 - slots codes can be made up using 2 letters followed by 2 digits followed by 2 letters where All of the following conditions must be met:
a. the allowable letters are A through G
b. the allowable digits are 2 through 7
c. no digit can be repeated
So we have 7 letters, and 6 digits
number of codes = 7x6 x 6x5 x 5x4
= 42(30)(20) = 25200
To find the number of 6-slot codes that can be made up using 2 letters followed by 2 digits followed by 2 letters, where certain conditions must be met, we can break down the problem into smaller steps.
Step 1: Count the number of allowable letters.
In this case, the allowable letters are A through G. Therefore, we have a total of 7 allowable letters.
Step 2: Count the number of allowable digits.
In this case, the allowable digits are 2 through 7. Therefore, we have a total of 6 allowable digits.
Step 3: Count the number of ways to arrange the letters in the code.
Since the first and last slots are for letters, we have 7 options for the first slot and 7 options for the last slot.
Step 4: Count the number of ways to arrange the digits in the code.
The second and third slots are for digits, and no digit can be repeated.
For the second slot, we have 6 options (all the allowable digits except the one used in the first slot). For the third slot, we have 5 options (all the allowable digits except the ones used in the first and second slots).
Step 5: Multiply the number of options from each step.
To find the total number of 6-slot codes that can be made, we multiply the number of options from each step.
Total number of 6-slot codes = Number of options for letters * Number of options for digits * Number of options for letters
Total number of 6-slot codes = 7 * 6 * 5
Therefore, the answer is 210. There are 210 different 6-slot codes that can be made up using 2 letters followed by 2 digits followed by 2 letters, considering the given conditions.