A 6 digit passcode is to be used for entry into an office building. Francis plans to select her passcode in such a way that the 6 digit code ends with an even digit, has all 6 digits distinct, and does not contain any digit greater than 7. How many ways can Francis select her code?

Question

kropot72 · Answer

Assuming that the selection is made from the 8 digits 0, 1, 2, 3, 4, 5, 6, 7, and that there are no repeated digits:
If the 6 digit code ends with 0 there are 7! permutations of the 7 remaining digits taken 6 at a time.
If the 6 digit code ends with 2 there are also 7! permutations of the 7 remaining digits taken 6 at a time.
If the 6 digit code ends with 4 there are also 7! permutations of the 7 remaining digits taken 6 at a time.
If the 6 digit code ends with 6 there are also 7! permutations of the 7 remaining digits taken 6 at a time.
Therefore the total number of ways of selecting the code is
$$4\times7\times6\times5\times4\times3\times2\times1=you\ can\ calculate$$

anonymous · Answer

Hi thanks I figured it out, buy you are off by a factor of 2. It is twice what you calculated. 
7x6x5x4x3 (for all those ending with 0)
7x6x5x4x3x3 (for all those ending with 2, 4, or 6)

kropot72 · Answer

Perhaps I don't understand the question. Can you explain why the number of ways with 0 as the end digit be different from the number of ways for for permutations ending with each of the other even digits?