MHB Solve 6-Digit Combinations Question with 0-9

[greprep]

"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)?

 

[MarkFL]

"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)?

You're close, but I would begin by filling in the first and last digits first (5 choices for each), and then fill in the remaining digits:

$$N=(5)(8)(7)(6)(5)(5)=\,?$$

 

[greprep]

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?

 

[MarkFL]

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?

Yes, that's what I was suggesting. :)