Question

Hey, I am facing a problem with probabilities

A student wrote a six digit number, which consists of numbers 1,2,3,4,5,6 on the board (the digits in the number don't repeat). What is the probability that the number can be divided by 6?

I know that there is 720 ways to write down this number (6!), any more tips how can I find the probability?

Answer 1

@hartnn

Answer 2

if a number is divisible by 3 and 2 it is divisible by 6.
any combination of 1 2 3 4 5 6 is divisible by 3 ( sum them -> get 21 . 21 is divisible by 3).
now, you need to find how many options will give you a number which is divisible by 2 (even number)

Answer 3

can you do it ?

Answer 4

I will try,sorry I was away

Answer 5

so the last digit could be written in 3 different ways (2,4,6),right?

Answer 6

yes

Answer 7

so maybe something like this (I am not sure)

18 even numbers?