- #1
Matejxx1
- 72
- 1
Homework Statement
From the numbers 4,5,6,8,9 we make 5 digits numbers (each number can be used only once).
h)How many of these numbers are divisible by 8?
The correct answer is 20
Homework Equations
a number is divisible by 8 if the last 3 digits are divisible by 8
If the hundreds digit is even, examine the number formed by the last two digits.
If the hundreds digit is odd, examine the number obtained by the last two digits plus 4
The Attempt at a Solution
Ok, so I started by trying to figure out how many number we could make that are divisible by 8
I divided the problem into 2 parts. First I calculated the possibilities if the hundredth digit is a odd number and then I did the same thing for the even number
a) since we have 3 even number there are 3 possibilities for the hundredth digit
and we also know that the other 2 number have to be divisible by 8 so that left me with 4 options (48,56,64,96)
so when I combined the hundredth number and these for options we get 3*4=12 options in total
b) we have 2 odd numbers so there are 2 possibilities for the hundredth digit
and we also know that the other 2 number + 4 have to be divisible by 8 so I got 2 options (68,84)
so when I combined the whole thing I got 2*2= 4 options in total
and this is where it kinda gets confusing for me I know that we have 16 numbers that can be divisible by 8 I got that from adding the even and odd parts together. Later on I figured that the first and second number can also be switched between themselves and that would not effect the first tree digits at all so I tried doing this
2!+12+2!+4=16+2*2!=16+4=20
I'm kinda wondering if this is an acceptable way of solving this because we never solved anything like this in school
and I would also like to see if any of you guys could give a more straightforward way of solving this because if this is right it seems way to complicated of a way of solving
Thanks for any feedback