Jacob is tasked with creating a 6-digit bank code using the digits 0-9, where the first digit must be odd and the last digit must be even, with no digit repetition allowed. The calculation for the total number of unique codes is determined by the formula N=(5)(8)(7)(6)(5)(5), where 5 choices are available for the first digit (odd), 5 for the last digit (even), and the remaining digits are filled sequentially from the remaining available choices. This structured approach ensures all conditions are met while maximizing the number of unique combinations.
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greprep said:"Jacob needs to create a 6-digit code for his bank account using the digits from 0 to 9. He wants the first digit to be odd and the last digit to be even. If he does not repeat any digits, how many different 6-digit codes could Jacob create?"
Would the best way to solve this be: (5)(9)(8)(7)(6)(4)?
greprep said:Oh, I see. So I would put in 5 first for the potential odd number (1,3,5,7,9), then 5 at the end for the potential even numbers (0,2,4,6,8), and that leaves us with 10-2 (8) choices for the second, 7 for the third, 6 for the 4th, etc?