Question

find how many six-digit numbers can be formed from the digits 2,3,4,5,6,7 (with repetitions) if a) numbers formed must be even b) the numbers formed must be divisble by 25 c) the odd digits must occupy even position (2nd, 4th, 6th) and the even digits must occupy odd positions (1st, 3rd, 5th)

Answer 1

a) to be even, the unit digit must be even
so you have 3 evens
and since you can repeat any number, you will have
6*6*6*6*6*3 =

b) if a number is divisible by 25 it must end in 25, so what would be left over for the other spots?
c) so the number must look like this:
EOEOEO , fill in the spaces.

Answer 2

a)23328
b) 2592
c) 729