This is a problem from my text. Of course my teacher expects us to know the answers without being taught how to do them, so i ask here.

1.) Find the number of passwords that use each of the digits 3,4,5,6,7,8,9

So for passwords i would think order matters so i use the permutation eqn n!/(n-r)! which is 7!/(7-7)!=5040 cause we have 7 numbers to choose from.

now

in how many passwords

a) are the first three digits even?

b) are the three even digits consecutive?

c) are the four odd digits consecutive?

d) are no tow odd digits consecutive?